Paul has no chance of winning the election as a third party candidate. He'd have trouble even getting on the ballot in some states, for one thing. And he'd get even less media coverage as a third party candidate than he gets now as a Republican.
However, the longer Paul remains in the race, the more he gets his message out through "alternative" media. I think that Paul realizes that his role right now is to build a movement and promote a cause, so that 4 or 8 years down the line, somebody with his views will actually have a shot at the Presidency. For this reason (and only this one), I'd like to see him run third party.