It might be tricky if you actually use git elsewhere -- not sure what would happen if you have a repo that contains other repos. For instance all of the hidden .git files would need to get synced. That should work, but will br annoying to fix if you ever have to merge manually.
Otherwise... it should be possible to have the Documents folder be a top level repo, this should be doable now in stash.. To add all files, you would have to do a
git add *
git add */*
....
git add */*/*/*/*/*/*.....
(or else we could add a new switch to git add that does a full tree walk). You will need to be diligent about always doing a git pull before starting work on a device, and a commit and push when finished, otherwise you will easily get out of sync and have to use merge... while get merge does work in stash, It can be tricky, and ai am not sure how many people have actually used it other than me. It is also embarrassingly easy to cause work to be lost in the current stash git implementation.