I don't think it's a good idea. Cats don't have to have claws to overpower a bird, they have pretty nimble arms and paws. We had a big (15 lb) ginger cat who didn't like mr. g'bag doing stretching exercises before his softball games and would attack his ankle and calf. He held on so tight I had to pry him off his leg.
Cats aren't evil but they invent games for themselves. They like to play hunt in the house, but they could pose a danger to semi-small birds with hollow bones. The bird will be curious about the cat and vice versa, they could be great pals. When I was a kid I had a parakeet who would perch on the cocker spaniels head. The dog let her horse around with his teeth and ears, but there was one day the bird was flying low thru the house, when she flew toward the dogs head he grabbed he with his mouth. My mother stated screaming and took the bird out of Benji's mouth. I don't think the dog meant to hurt her, he just stood shook still like he shocked himself. The bird was fine, and I don't remember any more incidents. But anytime you have 2 different species as pets, you need to be very vigilant.