Yes, but it's closest we'll ever know since odds are there'll never be a more "official" answer.

no Mark Patton said HE THINKS Jesse survived its never actually said for sure

Well, the Doctor in the 3rd movie was probably going to jail as well since he was the last one to see most Nancy alive and stuff.
The actor says that Jesse and Lisa got away from Freddy and lived happily ever after, so odds are that last scene was just a random nightmare and they left town.

He should probably be in jail. Very poor police work to not connect the teenager they found high as a kite covered in blood with the dead school teacher. Suspiciously there are several more times in the film he is covered in blood after a murder. Personally I think he woke up from his last nightmare to find the bus surrounded by a SWAT team and he was promptly placed into custody. He would have seemed nuts at the trial and ended up in funny farm. Maybe even the same funny farm all the kids are at in Part 3. There's fan speculation that the teenager mentioned in Part 3 who "died after removing his eyelids with a razor blade" was Jesse Walsh. That's the closest to an answer you're going to get.

It's not clear. But I like to think that last scene was just Freddy giving Jesse one last nightmare.

Or buggered him to death.

Freddy probably killed him

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