If you look at most firing pins, they have a taper to them. Each non stopped cycle drives it deeper into the taper.
Certainly a few dry fires does not hurt it, but if you do it much over time, then yes (if it has a square shoulder that is different).
So, it you want to do it fairly often then a snap cap is cheap avoidance.
note: pistols are a different story and dry firing is ok for most of them (probably some exceptions like a Lugger that has all matching numbered parts)