That would work for a small shelter as long as the quail are also in a pen or aviary. They would use that for shelter only. Quail don't roost up for the night in coops per say, unless they feel the need to do so. If you added some hay, they would definitely use it for laying eggs.
What are the dimensions, Also It depends on which species of quail you plan on owning. Coturnix and Button require less space than say Bobwhite or Valley.
And It also depends on the size of the run you have attached to the coop.