When you say "cover" your nest boxes, are you simply talking about blocking them off??? At four weeks, your chicks probably won't even use the roosts yet. I don't think mine roosted (on my real roost) until they were about two months old. If you're nest boxes are on the floor, the may go inside them, so I would block them off. But if they're elevated nest boxes, you probably won't have to worry about it (at least anytime soon). Do make sure your roosts are higher than your nest box perch, and they will prefer the roost.
Now if you're talking covered nest boxes verses open nest boxes, I would say to cover so that, when your birds get a little bigger, they don't perch on the dividers of the boxes, which could result in poop in the nests.