Firstly, I am not wild about the idea of a "real Sean Fentriss" (see below). Call Sean Prime the Sean Fentriss in the world the movie takes place in - the one where Source Code is being run to try and prevent a second terrorist attack. That guy is dead - the train exploded and he was on it.
What happens to all of the Sean Betas (and Sean Gamms, and. . . well see below)?
The answer to that is dependent on what you think is actually happening in Source Code.
Hypothetical model #1, which is pretty much what Keith described:
If you think that every time the simulation is run that a new universe is spun into existence, then Sean Fentress is probably ceasing to be once Colter "jumps in". The parameters for the creation of this universe are such that Sean Fentriss will never survive in it unless Colter alters the course of events - something he only manages to do once. Want to get freaky? Recall the end, where Colter-As-Fentriss (Sean N, if you will) calls that universe's version of the Source Code project and asks Veriga Farma to take care of that Coulter. We'll call him Coulter N. What if Universe N's source code project gets activated for another disaster down the road? The cycle repeats itself, only this time we're talking about jumping into some other guy. Paul Smithson. Paul N becomes a bunch of Paul N1, Paul N2 - Paul Gammas, if you will in the universes further spawned by activation of Source Code in Universe N. Paul's fate is the same as Sean's. He misses on all the future in every case.
Second Model:
If you think that what is happening is that Colter is actually appearing in a parallel universe, then Sean^N is definitely ceasing to be. But there are an infinite number of Seans out there. It holds that not all of them die on that train. In fact, there will be realities where that terrorist doesn't even exist. There may even be an intelligent cyborg-Dinosaur-Sean out there somewhere! Ok, I'm being silly on the last one. Anyway, any universe that Colter slides into appears to lose it's Sean. In most cases, that's because of the bomb on the train. But if Colter manages to stick around, I guess Sean ceases to be. Poor Sean!
In either case, I would consider all of these Seans "real".
I don't believe we have any real idea what is going on in Source Code (that is, I believe the movie leaves it up for us to decide what is going on); my own personal theory is basically Keith's. I really liked the movie though. I was expecting your basic action movie but got something more thoughtful.