I had a paid registration with add-ons but then toggled it to FREE and the add-ons remain. I believe this is causing some issues as I attempted to register some test and received a message that the participant was already registered (but they weren't).
It may be better to make it Paid with a $0 registration to allow add-ons on top of a FREE event.
I don't know the full extent and may not be very common - it's just a little gunky at first try.