Funny you should ask that. Because, football geek that I am, I recently ran an American football simulation program I got from the Internet. And the clock did not run during the PAT simulations. So I'm thinking that PAT's freeze the clock. If that's wrong, perhaps someone will correct me.
The clock does not run during PATs. That is true even if it is a blocked PAT and run for 2 points in favor of the defenders or, for that matter, in the case of an attempted 2-point conversion.
I know you can't take your sweet time to get a PAT, but in regulation, if you score a game-tying TD, and the clock is at zero, you are allowed to kick even with no time, to win the game.
I thought the PAT was always "off the clock" so to speak.
Maybe with a two point conversion, there's some 40 second time limit.
That would make sense, as if a QB didn't like what he saw lined up against him, the coach could change his mind and try a single point kick.