If you don't train the cat to do "tricks" it wont do tricks obviously. Same thing goes for dogs.

Getting back the the original question now.. Its fine to have cat(s) and bird(s) as long as they don't meet each other.. in most cases the cat would attack it but thats instinct. My cat isnt allowed to come upstairs (for other reasons then my birds) and shes been quite good about that, but now that I do have birds shes been sneaking up every so often. Whenever I'm going to let my birds out I close the basement door because of the slight chance of her coming up. So like I've said (and the others) when you do get your new kitty be very cautious about your birds and it. Good luck to you and your new baby =].