Is it possible...

for a hitter who had no triples in real life to get a triple off of a pitcher's card in the sim?

yes

I think there is even a chance to get a triple off a double on his own card if there was a player on first who tried to take an extra base.

Not sure though.

I think there is even a chance to get a triple off a double on his own card if there was a player on first who tried to take an extra base.

Not sure though.

A hitter can take third in this situation (when the throw goes home on a double), but the batter is only credited with a double.

Another way a hitter with no triples can get one in this sim is a flyball X to a 4- or 5-rated outfielder.

Many managers used to use triples as a way of determining what card a player is on in the Mystery Card format. Because of the reasons already given here, and others, I have never found triples to be a good indicator of anything.