If someone else actually ends up winning delegates, they'd have to REALLY hate Trump...
Past primary challengers to incumbent presidents who actually made it on the ballot in most states (Reagan '76, Kennedy '80, Buchanan '92) all ended up endorsing the president they were running against in the general election.
That said, Trump is a weird case. ~1/5th of the GOP caucus in the Senate didn't endorse him in the GE last time, and he won anyway.
Also, if, say, Kasich is running against Trump in 2020, the question will be posed both ways: Kasich will be asked if he'll endorse Trump in the GE if Trump is nominated, and Trump will be asked the same of Kasich if Kasich is nominated. I doubt Trump agrees to endorse Kasich in the unlikely event that Kasich is nominated, so Kasich might just reciprocate and say he wouldn't endorse Trump either.....
How the RNC chair responds to candidates refusing to pledge support for the party regardless of who win the nomination, I don't know. Aren't there even some state primaries where such a pledge is required for ballot access?