Yes! I keep thinking how cool it would've been to see Rose and the Master interact, but then I can't really see how it would work in canon, because they both fulfill similar functions to the Doctor. They're central to him emotionally, though in very different ways. I honestly don't know what he'd do if he had to choose between them, which one to prioritize. He's so obsessively needy about both.

And usually the Doctor's big emotional arc is connected to the companion, but in S3 it was connected to the Master. (Martha's emotional arc was related to the Doctor, but the Doctor's really wasn't that connected to Martha). It wouldn't have worked as well if Rose had been there the whole time--the fact that the Doctor was so emotionally disconnected from everyone else made his desperate need for the Master even more intense and powerful.