I raise heritage breeds. I love them, but they do drive me nuts! They have been sleeping all winter in an Aspen tree in my yard. Some sleep on my roof. So yes, the non-double breasted varieties can fly. Not like a wild turkey, but they can get over fencing, on top of the roof, up into trees. We started attempting to catch them all before they roosted and sticking them back in their coop - but we gave up fighting nature. Through snow storms and sub freezing temps, we haven't lost a single on to sleeping in the trees.
Last year's birds took to a different spot and slept along a fenceline. Even when we rounded them all up, in the morning, they would hop the fance and roam off into the neighbor's field to lay eggs. Most of them, eventually, did not return and were dinner for the coyotes. SO I am hoping this year, if they want to live in my trees, maybe they will at least stay home. If not, I'll need to build a run, too. But I am not inclined to do so, I raise 120 turkeys each year and keep 30-40 for breeding. That's a pretty big run to make those turkeys happy....
CHickens are trainable. I've been able to lock them in a coop for a day or two, and they figure out that they are supposed to go there to sleep. Turkeys - we locked them up for 2 weeks, and as soon as we let them out, they went back to the trees. Stubborn! But I love them!