Do you garden? I have several raised beds (and am making more). I move my quail pens about once every 3-4 months. My quail know me and since one garden bed is pretty much the same as another and their pen and all of the furnishings move with them, they don't all take a break from laying and...
Yes, it can. Quail don't like change, so the less you move them the better. If they trust you a lot their break from laying will be shorter, but you can expect up to a two week break after making serious changes to their environment.