If you are going to try, and you really are trying to win, the third party candidate should run as such from the get-go. A candidate that has already failed to win 50+% of the Republicans, will have a hard time winning a majority of both republicans and democrats. Unless there are significant revelations after the primary with regards to the party’s nominee, someone who loses the primary then comes back to run third party against the winner is only showing their disgust with the nominee.
The exception to that is the Lieberman scenario, where the party rigs the nomination, so that the candidate most desired even by members of THAT party ends up running independent, especially if the party in question is dominant in that state. Kind of a perfect storm type situation and doesn't come together very often, I know.