We kept a single peahen with our chickens when we lived in the desert, and about the only loud noise she ever made was "SPONK!" when something alarmed her. However, once we added a peacock and the flock multiplied--oh how they multiply--I've heard the hens occasionally holler like the males. So they can do it, but it's rare.
One problem with running peafowl with chickens is that if your chickens pick up cecal worm, the peas can get it too, and sometimes will get pretty sick. We were fine in the desert, but when we moved to a more humid climate and clay soil, there were earthworms everywhere (they're the vector) and eventually we did have a juvenile pea come down sick.
