Close enough, it's been years since I played it!
As for
T2, yes, he was in a dream sequence while Sarah's at the mental institute that was added back into the extended cut. It was a nice little scene (and it explained the whole "no fate" speech, which Sarah claims he gave to her even though he never actually said it in the first movie) but it didn't really add much, plus it relied on you knowing who Biehn was from the first film, so I can see why it got cut.