Registering it again is a small endeavor, so just do it if in doubt. I did the same thing just to be sure, so the question isn't all that stupid.
In theory I think nothing probably should break as you flash something else on the device (which is than in charge of handling the fingerprints to the apps), but seeing many people having many problems with it I didn't want to take the risk as I don't know how it works on a hardware level. If the fingerprint module stores them itself, it could mean problems was my thought.