Do you think it is appropriate to also invite the priest to the wedding rehearsal dinner and the reception?
I was always raised not to crash a party and so if I do not receive an invitation to the rehearsal dinner or the reception I do not go. Even if I am invited the day of the rehearsal or the reception (which happens more often than you might think), I do not go; nobody likes to be an after thought.
Think about it this way. You send an invitation to your third cousin twice-removed (whatever that means), whom you have not seen in a decade and do not especially care if he or she attends; you send them an invitation simply to be polite, lest they feel slighted.
Presumably, you want the priest to attend the rehearsal dinner and the reception so he, too, ought to receive an invitation. It is simply good form.
Certainly, not every priest will stay away if not invited as I do (for me, this extends to more than just weddings), but I am sure receiving an invitation will not offend him. It might even brighten his day that you want him to be at the events enough to invite him, rather than simply expect him.