No that isn’t going to happen, clergy are not an official position for any government office, they do the marriages that they want to do.
People don’t just go into churches and demand to get married, like they can with a government official, who isn’t his own boss.
Just like they can't go into a bakery and demand they be sold a cake. Oh wait, never mind...
As I said before, if you think Catholic priests will not be forced into performing gay marriages lest they be stripped of their right to perform marriages recognized by the state, you're kidding yourself.