Yes, it can. You will have to give them time to adjust. It may help to place an egg or two in the new nest boxes.
One other thought regarding the lighting, although you may know this already. Make sure your winter lighting is from the "warm" end of the light spectrum. These new bulbs that are out there come in "cool" or daylight, and "warm". I bought one labeled daylight once thinking it was, well, daylight. I couldn't figure out why the hens hadn't started laying. I suspected the lighting and sure enough, when I checked the packaging those bulbs were "cool". From what I have read, chickens don't respond to light from the "cool" end of the light spectrum.