I think there is a risk (not necessarily absolute) of stressing the poor guy out--having a cat stare at him constantly may be frightening to an especially shy BP. I think it all depends on how your BP reacts.

A cat's still a predator, and a snake is lower on it's food chain. (unless it's a huge one!)

That said, I banned my cats from my room but at EVERY chance they get, they'll run/sneak/trample their way in to stare at my empty glass tank--my corn used to live there before I moved... and they'll sit there for HOURS thinking there's still something in there.

Silly creatures.