Vertically speaking, bricks are a covering material not a structured wall material. The third little pig's house of bricks probably had stick-frame walls rather than unstable stacks of bricks. Bricks are usually attached to block or wood walls with metal tabs and mortar.
I see no reason not to use the bricks as a care-free cover over the cheapest building material when constructing your coop. I could imagine a neat coop to match my brick facade house. (drooling here)
Love, Linn B (aka Smart Red) Gardening zone 5a - 4b in south-est, central-est Wisconsin