Many people put down scrap vinyl flooring, so that dropping moisture doesn't soak into the plywood flooring. So you're talking about just putting the skin of counter laminate down like some do vinyl flooring? That should work. As Pat mentioned though, unless your coop is about 40 inches tall, you probably won't be able to swing a dropping board. You want your chickens to have about 18 inches of headroom on the roost, and they would need 18 inches under the dropping board, and you want your dropping board at least a few inches below your roost. So if your coop isn't very tall, then I think I'd just clean the droppings from under the bedding each day.
