No.
It would depend on who the other Republican, the one with 37 EV, was.
What if it was Paul Ryan? What if it was Mitt Romney?
I have zero confidence in the "Republican" House in such a scenario.
We know of at least five high profile schemers in the Republican Party who would very likely go along with such a thing. Romney, Ryan, McCain, Graham and McMullen. They’ve been trying to derail Trump since the primaries. Complacency about this being rejected in the House if it gets that far is not a good idea, in my opinion.
“I have zero confidence in the “Republican” House in such a scenario.”
No argument here. I would like to hope though, that at a minimum, the GOP side of the House would select a Republican. But, agree that the risk of a RINO being selected would be real.