If there is food available, they will. My Mom's neighborhood had a hawk living in an enormous spruce tree last year. It picked off all of the quail who were living there. (Quail are cute, but dumber than rocks...sigh...) Totally suburban area in a city of about 250k.
Our area hosts a pair of redtails. We've seen them several times; once when one of them dropped into our back yard and hit some underground critter, a mole or gopher. He flew away with some small animal in his claws, anyway. And the plague of moles/gophers that used to tunnel all over our property is gone.
I've also had a juvenile redtail take a male cardinal right off my back deck, underneath the feeder. I'd been doing something in the kitchen, heard a THUMP
against the window, and looked out to find the hawk on the deck with the cardinal in his claws. There were red feathers stuck to the window with blood. The hawk must have startled the feeder birds and they scattered. The cardinal made the mistake of thinking that the window was an escape route, and the hawk grabbed him while he was stunned. I considered for a second whether I should attempt a rescue, but it was obvious that while the cardinal was still alive, it was badly injured and would probably die anyway. The hawk took the decision out of my hands and flew away with the cardinal.
I also had a female peregrine attempt to take a kitten that was sunning himself in the window. That he was inside the glass was the only thing that saved him. Again, a huge WHUMP against the glass, and a rather stunned and disoriented falcon. I kept an eye on her until she recovered and flew up into one of the trees. Had she not come out of it in a few minutes, I'd have called a wildlife rescue organization.