Today, Randy Seaver wrote a blog post about how RootsMagic Can Import Sources From FamilySearch Family Tree.
He gives an example and shows a screen where he compares RootsMagic Sources on the left with FamilySearch Sources on the right and then shows how he added a source from FamilySearch to his RootsMagic database.
In conclusion, he says source citations from FamilySearch can be added through a relatively simple multi-step process, but not "automatically".
Now if, as was posed in the question, Ancestral Quest and Legacy both download sources in a similar manner, i.e. not automatically, then those 3 programs will not do the trick.
However, the fact that sources can be downloaded in entirety as shown by Randy, says that the API (Application Programming Interface) provided by FamilySearch does allow the retrieval of all the source information.
There are other full family tree programs among the FamilySearch approved "Apps" in their App Gallery that likely also download sources. It is possible one of them have been programmed to download them automatically. You can check: Familienbuch, Family Tree Builder, Family.me, MacFamilyTree and WikiTree. (MagiTree would have been another one, but it is no longer available.) I believe all those programs can export GEDCOM, so if you find one of them can download your sources automatically, then you can use it to efficiently retrieve all your sources from FamilySearch.
If not, then it is likely a matter of time. I'm sure users will request this of the programs they use. I know of at least one program that is planning one day to include automatic downloads from FamilySearch of all data including sources.