Frist has a shot of winning the nomination; it's not a good one, but it's there.
He has virtually no shot at winning the election.
J. J. Third Rule of Politics might end up being: "To be elected president, you must have been Vice President or a Governor."
That has described every presidential victor since 1964. :-)
Frist is neither.
Out of curiosity, have there been any presidents who were not previously a governor, senator, general, veep, or cabinet member?
I would say Frist has a nonzero chance at the nomination, but I'm not sure how far it goes beyond that unless he either gets an endorsement from Bush, or backed by Rove.