“When a party receives the conservative vote regardless of the candidate, do you think that makes it more or less likely that the party will run a genuine small government conservative?”
I’m assuming your goal is to have a conservative small government candidate run AND WIN, not simply run.
IF that party gets elected and if conservatives within that party work to shift it more towards conservatism ... Yes
IF that party does not get elected, or you decide to abandon working within it, you have NO chance of reaching your goal.