Actually, yes, they do. They could call themselves a priest, but legally they would not be, and they would not be a member of the Catholic (big C, is an important difference) Church, and thus would not be a Catholic priest even if they started their own religion or joined another one . . . they'd be some other sort of priest.
The Catholic Church, along with other churches, also has a procedure known as defrocking, which does not excommunicate someone, but simply removes them from being a priest (or other ordained ministry).
Exactly. They would be christian priests if they want to, sure, but not Catholic priests. In the days, an excommunicated person was a persona non grata of the lowest social status.
