Yes, absolutely and without a problem.

Vantablack is effectively a black body, and it's at room temperature with no need for radiation protection or worries about an event horizon.

The thing is, a black body doesn't mean it emits no light. Instead, it absorbs all light and emits black-body radiation - a certain spectrum which depends only on its temperature.

A hot piece of iron in the foundry glows due to its black-body radiation.

A cat is at body temperature, which very close to that of people.

https://en.wikipedia.org/wiki/Black-body_radiation#Human-bod... works out that the peak wavelength for black-body light from humans is 9.50 µm - infrared.

Humans can't see infrared, and very little of the energy comes in the form of visible light.

So your hypothetical cat would look like a black shadow, but would purr and be no problem to pet.

So, the cat will Be at room temp and no worries about the radiation.

Nice!!

Well, the cat will be at cat temp, which is warmer than the room.

Cover a cat with Vantablack and you'll be close to your black-body cat.

(Be aware that this might not be good for the cat: it might make the cat too hot, I don't know the toxicity, I don't know how it affects self-grooming, etc.)