I'm told that rag doll cats don't hunt. Maybe because they're too big and placid (like Garfield) to go to the effort?
Enjoy your baby cockatiel. They can be noisy. Sometimes our budgies get noisy, but they are nothing compared to a cockatiel.
You can teach a cockatiel to not only say words, but to understand them and even use them to ask for things (such as millet sprays). An Aussie TV vet, Dr Harry, did a segment on the show where he demonstrated how to teach a cockatiel to say "millet" when it wants some.
Our budgies have the free fly of the house, but go back to the cage and are shut in at night. We have to be very careful about open doors and windows, making sure all are screened and we don't have doors to the outside open with budgie access. We had our male budgie get out about a year ago when easy child 2/difficult child 2 arrived to do some wedding planning. The door was open for a little bit too long and Buddy flew out. Almost immediately a Butcher Bird was on his tail. We think the only reason Buddy didn't get taken immediately, was he showed no fear of the Butcher Bird. They don't LOOK like predators at first glance. Also, we'd been in the habit of putting a vase of native flowers on Buddy's play gym, and as we picked those flowers form our garden, Buddy flew to those and began to nibble. So difficult child 3 was able to go to his bird (who had been trained to step up) and get him back. It was a near thing - if he hadn't been so tame, plus hadn't been such a cheeky bird with confidence, we probably would have lost him. he wouldn't have survived more than an hour or so. That Butcher Bird was moving in for the kill.
Where budgies live in Australia, we don't have Butcher Birds. We do have wild Cockatiels in this part of Australia but I haven't seen any for years. I think we have too many Butcher Birds.
Abbey's birds are big enough to scare a cat. We have wild Rainbow Lorikeets here, they can also deal with a cat even though they would be smaller than Abbey's. But our Lorikeets are the soccer hooligans of the parrot world, they will beat up on a Cockatoo... I've seen it. They probably keep the Cockatiels away too.
Marg