Edwards would not win. He wasn't going to be re-elected in NC as it was, which would have been a crushing blow to any future political career. His best decision was to accept the VP slot and take his chances with Kerry. While he's a pretty boy and lovable, he's weak on many national political levels.
Unfortunately, you're probably right. Edwards, while a very good politician, doesn't have much experience on the national level. If he wants any chance or a better chance than what he has now, he needs to run for Governor of North Carolina. I doubt he would win that, but stranger things have happened.