2001 began filming before Trek premiered on television. How likely is it that Kubrick et al in the UK got a chance to see Enterprise designs? It's possible that someone might have seen advance Trek publicity, but I don't know how likely that was.
But Star Trek was in front of the public for two years before 2001 was released. That's a long lead time. If the Enterprise had a spherical hull similar to the Discovery, I think Kubrick would sent his design guy back to the drawing board to come up with something that could accommodate the interior sets, but differently. And he'd reshoot the fx. And MGM would have been furious about it, and they'd want to know if Desilu had ripped them off.