I would like this idea. I know a lot of 2K basketball games have done this pretty well and NBA live has tried things like this but I didn't like theirs as well.
However, unlike basketball games where there is one chemistry for the whole team I think several separate chemistries would work best here. Maybe an overall for offense, defense, and special teams but then a separate one for O-Line, D-line, LBs, DBs, QB to receivers, QB to line, RBs to line all of which would have a direct impact on that groups performance. For instance the giants line, they have been playing together a while now and have good enough chemistry that regardless what happens to the rest of the team they will be good together.