I really don't have enough information about your circumstances to be able to give you a definite answer. I'll try though.
Most chicks are fully feathered at 4 to 5 weeks old. Unless you have something unusual going on or severe weather, they should not need supplemental heat after that. I have no idea how cold your nights are inside the coop. Even if your nights are fairly warm, I'd provide supplemental heat until they feather out.
Chickens of any age usually do not do really well when sleeping in a draft or breeze unless the nights are reasonably warm. I've seen chickens sleep in trees when the night-time temperatures got down to zero Farenheit, but they were in a well protected valley. But basically when they are young, it is best to keep them out of breezes until they are older, even if they are fully feathered.
My brooder raised chicks usually do not roost until they are 10 to 12 weeks old, so expect yours to sleep in a pile on the floor when you first put them out there. If they have some nice bedding to scrunch down in, like wood shavings or straw, they can do a pretty good job of keeping themselves warm.
How well are yours acclimated? Are they used to a temperature swing or do you keep them at very warm temperatures all the time? I normally keep one area in my brooder the right temperature but the far corners are usually 20 to 30 degrees cooler. It is not that big a shock to mine when I remove the heat.
So, can you put them out in the new coop before they are feathered out? I would not without supplemental heat, but you might get away with it. A lot depends on what the coop looks like an your weather. I do think you are taking a risk.