Even if you do screw it up, the commit should all be there and valid. The only thing that happens is HEAD won't point to the right commit on other boxes, and then when you do sync you'll clobber the file containing the commit for HEAD, thus losing the other commits. Fortunately, they'll still exist until a gc occurs, so you can go find them in reflog.
Correct, I still had my HEAD files, but everything else seemed pretty broken. I'm not a Git expert by a long shot, but I would imagine that Dropbox renamed some files like "Foo.bar (Eli's Conflicted Copy)" and that really confused the history.
