Yea, and the sooner after hatch the better. I keep mine in the incubator/brooder for no more than a day (just long enough to fluff up and not be wobbly anymore - also makes sure they're more likely to survive IMO), then put them under mom. Some hens are just fine with this, some hens are not...
I haven't had eggs chirp much unless they were cold (by accident I found this out). However, I have had an incubator chick hatch and dry off in the incubator, then I took it outside to pop under moma hen. She had two babies already but they were only about two days old. She heard the...