You need not speculate on what would happen. The experiment has been tried a few times, with the following results:
1992: 106,152 votes / 5th place
1996: 184,820 votes / 5th place
2000: 98,022 votes / 6th place
2004: 144,498 votes / 5th place
Your premise falls apart in light of the fact that the Christians never left the GOP during any of those elections.