2020 Update: For the content in this answer, assume that the user has an account with FamilySearch and has logged in to their account.
2017 Update: As of September 7, 2017, FamilySearch has discontinued distribution of microfilm. They are transitioning to digital records access. For the announcement on the transition, see the FamilySearch Newsroom article UPDATE: FamilySearch Digital Records Access Replacing Microfilm and the accompanying FAQ: Digital Records Access Replacing Microfilm.
As part of the transition, the FHL has introduced a new icon with a key that can be seen in the film notes on the far right (where we are used to seeing the looking glass, microfilm reel, or camera icons).

If you try to view the film from home with a public (non-LDS) account, you get the following message:

For the first roll of the collection Queens (New York) death certificates, 1898-1949, clicking on the camera-with-key icon gets this result:

The right to view the digital images from home depends on the particular collection and that is determined by the entity that holds the rights to the records, as you can see from the example below.
Some collections can be viewed online from home as long as you log in. This is what you see when accessing some of the Bishop's Transcripts provided to FamilySearch by the Devon County Council. In the search result, my sample result showed a document (for the extracted/indexed data) and camera icon without a key.

Once I log in to my public account, I can view the document. However, the download has been disabled, and the user is directed to contact Devon County Council for a copy of the image (thus preserving the income stream for the archive).

The other icon that wasn't discussed in the older answer can be seen in this screenshot of the Browse All Published Collections list:

The camera with a screen behind it indicates that the images can be viewed a a partner website (such as fold3).
My original answer (with all the previous updates) is below the line -- I am leaving it in place until the transition to digital is complete. During the transition, the microfilms which haven't been converted to digital yet -- the items which show up with a microfilm reel in the Film Notes but not with a camera -- will have to be viewed at the Family History Library (or a local FHC or FHL that happened to order a copy for themselves before the deadline).
Sometimes the Family Search Catalog entry for a record collection has a red message in the Notes section that will tell you if the collection is online; a link to the collection is included in that note.
The image has been taken from the handout for the class Using the
FamilySearch Catalog Effectively by research specialist Joni Kessler, AG®, presented at the Family History Library as part of the United States Research Seminar during October 2015:

Everything that follows was written before microfilm distribution was discontinued and some portions may be deprecated. (NB: July 2016 update at the very bottom of this answer.)
Thanks to AdrianB38's observation and a bit of digging about, this is what I've discovered so far.
- Adrian's example California, San Mateo County, naturalization records, 1856-1947 is described as a Manuscript/Manuscript on Digital Images and was a Digital capture by the Genealogical Society of Utah in 2010. This is why there is no microfilm. The catalog description and the Research Wiki have links to the digital images, which are available for browsing online. Some volumes are indexed in San Mateo County naturalization index, 1906-1945 / Trindle, Cath, and that index does link back to the online images.
- As noted in the original question, the catalog entry for Queens (New York) death certificates, 1898-1949 notes that there is a printed index: Index to deaths, New York City, 1888-1965. If I wanted to cross-check the certificate numbers with the ones I collected from Ancestry or the GGG, this seems to be the entry for the film I would need:
All boroughs 1900-1904 Family History Library United States & Canada
Film 1324914
Clicking on the linked number takes me to the ordering page. There are several components to the ordering page which are worth noting.
- a note advises the user "Please sign in to place an order or to see pricing specific to your area."
- another says "NOTE: Check the library catalog for more information and to check for a digital copy before ordering." which implies that there SHOULD be a link if a digital copy exists
- if I click on the linked words "library catalog" it does not take me to the library catalog -- I only get a header which reads "Search Results for FamilySearch Catalog" and the search form. So if you need to revisit the catalog listing, before checking that link, save the film number so you can paste it back into the search box.
- signing in and selecting my default FHC results in a note that the film I want is available there (not surprising for an index) and I don't have to order it (hooray)
- at the bottom of the screen it says
1 Record for Film 1324914:
1.Index to deaths, New York City, 1888-1965
New York (New York). Department of Health
I saw on the search for the death records themselves that there may be more than one record for a particular film number, and to get the one you want, you must also know the item number.
- In the midst of searching for these things, I discovered the Register of New York City death records. It is a digital copy of a printed reference work that lists what records were held by the FHL at the time of publication, with instructions on how to use the films and a list of the film numbers. 2019 update: This used to be viewable online but is no longer available due to copyright restrictions. The original can be viewed at the Family History Library [now the Family Search Library]; check the catalog for current information.
A note at the beginning advises the user that there is a partial index at Ancestry, and advises the reader to search their database because this is an ongoing project.
So it seems that the answer to my question is yes, the collections which are available to browse online should indeed be noted as such in the catalog. Thanks very much to AdrianB38, because seeing the case of the California records that he found, where the linkback does exist, gave me the example I needed to see how the catalog and the Research Wiki note the link where it exists.
Note: I'm not checking either one of our answers as the definitive one just yet, in the hopes that someone else answers who actually knows.
For those interested in the New York City Death records, there is a new index at New York, New York City Municipal Deaths, 1795-1949 wiki article which gives the reference number of the appropriate FHL microfilm, but there is no link to the film.
If you go to the main search page for the FamilySearch Catalog: https://familysearch.org/catalog-search
Immediately above the blue search, button, there are radio buttons for choosing where the records are available. The choices are:
- Any
- Online
- Family History Library
Choosing Online filters the catalog search results to the ones which can be viewed via FamilySearch.org.

Choosing the Family History Library causes a drop-down box to appear. The FHL is at the top, followed by a list of local Family History Centers, arranged alphabetically by the name of the center.

Local FHCs and FHLs (the larger centers are called Libraries) have pages on the FamilySearch Research Wiki which contain a box for Links relating to that center on the Wiki. Choose catalog and that should take you to the Wiki page about the catalog. If you see a note like this:
ANNOUNCING A MAJOR CHANGE
The CATALOG of the [placename] FamilySearch Library has MOVED!
Our catalog is now located at familysearch.org>Search>Catalog Under
“Search these Family History Centers” select [placename] FamilySearch
Library
The catalog allows patrons to:
- Search by Places, Surnames, Titles, Authors, Subjects or Keywords
- Broaden a search to other local Family History Centers or to the holdings of the Family History Library in Salt Lake City
- Have a direct link to the growing collection of online resources at FamilySearch.org and elsewhere
... then your local center's online catalog has been migrated, and it should show up in the drop-down box.
I've recently (July 2016) found a new case of images which are available online, for which the red click here link does not show up. I found the collection Obituary index, 1837-1969, created by the Toledo-Lucas County Public Library, by means of a place search with the filter set to online.
If you look at the film notes section, look at the two columns on the right hand side where it lists the FHL film numbers and the formats available:

Clicking the camera icon takes you to the digital images.
This does not show up in the "Browse All Published Collections" lists, which suggests to me that they haven't finished assembling the waypoints for Browsing the images.