By "sync" do you mean "TreeSync" with your AMT on Ancestry?
If so, how do you have it set? Manual or Auto?
Have you seen any issues where DropBox and TreeSync are fighting each other to update?
No. As I recall DropBox doesn't grab the file until the program (FTM) closes it. When it closes, DropBox grabs i and does it's "sync" (unrelated to TreeSync)
From comments - For the OP.
I agree and have had heard similar.