Classic D&D emulates many REH-esque tropes.
But I don't think the gameplay produces REH-esque stories.
Conan frequently succeeds by acting on instinct, by rejecting moderation or subtlety, and by imposing his will on the situation he find himself in. And in many of REH's stories he finds himself needing to choose between riches and doing the right thing, and he does the right thing.
Whereas classic D&D gameplay encourages caution, planning, and understanding the situation on the GM's terms and responding to that. It encourages being calculating and expedient. None of this is very REH-esque, in my experience.