I think he should try, but I'm not sure he's got the leg strength to be a sure thing.
The fact that we have Price taking kickoffs makes me worry about Stefanou's ability to put the kickoffs in the end zone consistently, which is going to be a major handicap. On the other hand, if he can consistently make FGs from 52 yards in, and he can at least put kickoffs inside the 5 consistently, he's probably got a real shot.
Either way, I highly doubt he's kicking for us next year, which definitely sucks. It would be nice to have him as a weapon for longer. Can't get past the fact that he's probably already older than most kickers in the league, even if kickers have a much longer lifespan in the pros than anyone else.