It may be possible, but it depends on several factors.
Firstly, how many relatives, both close and more distant ones (3rd cosuins and further) have tested and match with you. The more tested relatives you have, the easier it gets to determine where exactly (from which parent, grandparent and so on) a particular match comes from. If you're particularly interested in this one line, you need a test from someone who is also descendant from the same person, preferably someone closest to her in kinship. This would allow you to find out your matching chromosomes and segments, which in theory could be inherited from your 4th great grandparents. Because inheritance is random and different for every person, there is no other way of knowing which segments you've inherited from your 4th great grandmother.
Secondly, how well-researched are your other lines. If those distant matches then also match and triangulate both with you and your other relative, in the same segments, then that's a hint of a possible shared ancestor. But the problem is, you won't be able to tell who that shared ancestor is unless you and your matches have extensive and well-researched familytrees (it could as well be someone from your 4th great granfathers' side). Additional research may be needed to confirm your hypothesis.
Thirdly, how strong is your match. Autosomal DNA is reliable for determing closer (5th generation and closer) relationships. It may also work for some more distant relationships, but not always. The further back you go in time and generations, the less DNA you have inherited from those ancestors, to the point where inherited segments are just not big enough to be reliable for that purpose (generally speaking your matching segments need to be at least 7 cM or more to be reliable, the smaller they are, the more chances there are for coincidental, identical by chance, matches).
I'd suggest you start mapping out your matches one by one. This would allow you to group your matches in clusters and gives you a better overview of your matches. There's a great free tool for it that I highly recommend: dnapainter.com. It will take lots of time and work, but eventually you'll have a sort of a map of your DNA, making the identification of every new match easier in the future.