In this hypothetical, it would come down to how successful the retconned race change was. Part of the reason outside-media stories have some greater flexibility with race is because we’ve seen more than one be an otherwise direct adaptation, with the real cultural changes of the race-change being either more subtextual or malleable to the character’s portrayal. However, we have seen a few that have exposed how you can either screw up an attempt to address the change so badly that neither the old fans or the target demographic are happy - New 52 Wally West being a prominent example.
I’m a white guy, so I have limits on how well I could see Tim getting a race change in comics. But to me? If he remained a humble, nerdy kid from an upper middle class family, with a recognizable characterization and series of adventures and relationships, and his tenure as Robin occurred while he still lived with a dad who acted similarly to Pre-Flashpoint Jack Drake, he would more satisfactorily be a “real” Tim Drake than the New 52 one. And I feel like all that could be maintained while someone with more real-world authority than me incorporated the cultural experiences that would differ between a black kid and a white kid in America.
...I will say that I feel pretty bluntly like, if I were in charge of adaptations, I would avoid making Jason black unless a black writer I trusted well wanted to. Jason feels like he’d fall squarely into the expected racist pitfalls and stereotypes you’d expect because of his already “poor street kid” origin and more “thug”-like reputation compared to the rest of the family.