Plausible, but not likely in my opinion. Throughout his flashbacks you see he is a cop trying to get these guys turned in, and he's pretty happy about it. Why not try and stay alive?

No, that's cut-and-dry what happened. Just like how Mr. Orange had spent his whole life training to become an undercover cop, Mr. White had spent his whole life as a veteran criminal. He had connections, he knew people (Joe), and he had a respected position in the criminal enterprise. And he threw all of that away on the belief that Mr. Orange was an honest criminal. Mr. Orange recognized this, and under all the emotional duress, confessed to the man who was the most fatherly to him, the man who insisted that they stay with him and help him recover, the man who revealed his true name to him when he was never supposed to even think about doing that. Mr. Orange had gone through his career with the belief that the people who he was tricking were evil, irredeemable monsters. The bank job and Mr. White had emotionally confused him to the point that he did what all liars strive to do: confess. A more interesting question, in my opinion, is if Mr. Pink got away.

Okay, you've sold me on the idea. As for Mr. Pink getting away, I doubt it. The cops got there pretty quick. It's unusual for Tarantino to leave a loose end like that though.