If he picks it up at the two and stumbles into the endzone from his momentum, that would fall under the momentum exception, and if he is tackled in the endzone the dead-ball spot would be the two.
Better to have him stop, then run in on his own accord, or have the offensive player just bat the ball clean through the endzone (after it has hit the ground), or have the loose ball in the endzone batted by the offense, all of which result in a safety.
Returning to the OP:
The defense cannot score on a try in the NFL (the ball is dead if the defense gets possession or if a kick fails)
The defense can score on a try in NCAA. Any team who scores gets two points for a touchdown and one point for a safety or field goal. But the try is a special interval outside the game, and scores on the try do not affect who makes the next kickoff.
A two point defensive try touchdown is often called a “safety” because, hey, it’s worth two points just like a safety is and it’s scored by the defense, which safeties usually are, so it must be a safety, right? We call that “announcer-speak”. It doesn’t meet any of the definitions of a safety.
Too bad it doesn’t apply in the NFL. We could then have a wonderful situation.
It’s the last game of the season, and the tie-breaker for qualifying for the playoffs is down to point differential. Team A must win this last game by 4 or more points to qualify for the playoffs. On the last play of the game they score a TD to go up by one point. Even a two-point conversion will not be enough to get them into the playoffs. So they take a deliberate 1 pt safety on the conversion (awarded to the other team) to create a tie hoping they can win by a TD in overtime.
Hah! That would be entertaining to watch! QB drops back 97 yards, much to the confusion of sportscasters and audience alike (99% of whom are probably unaware of the one-point safety). I like it!
edit: For the record, Wikipedia states that there never has been a defensive one-point conversion safety, so a college score with a team scoring exactly one point is indeed a very, very long shot. I’m curious to know if college football videogames are programmed with this rule. Somebody go play NCAA whatever-its-called, go for a two-point conversion, and back your QB into the opposite endzone and see what happens.