You don't have to have an Irish pp to be Irish! It just entitles you to apply for one. There is a register but it is a bit more complex than just registering. There is a good guide upthread as to who can register. If you don't choose to subsequently apply for a pp you don't have to. You would still be Irish
True, but you wouldn't be able to prove to anyone you were Irish, so it wouldn't be much use for travel, freedom of movement etc.