Yes, I've got one from the '50s where it screws the chimes up if turned backwards (although there doesn't appear to be anything in the mechanism that can actually suffer damage as a result). If turned forwards it'll stay in sync, so long as I stop on every quarter hour for the chimes.
As there's no calendar functionality it's usually easier just to stop and restart when it next shows the correct time.
Thankfully the mainspring will run for about a week, so it doesn't need winding that often...