A few have used the drinking cup system with chickens, I don't know what type of drinking cup you are going to do though...I really do reccomend the little giant waterers because they allow the full submerging of the bill and nostrils of my ducks. If your drinking cop does this then great, Go for It! But if not, don't use them. My setup has been really nice, i just rake out debris in the morning before the ducks go outside and then stir the bedding in their coop after they are out and I'm pretty much done...except every other day I rinse out the water bowls and empty/refill their pool.
A note on the pool I use-specific to anybody who is wanting to run a gravity system from a 55 gallon rain barrel set up like mine:
I cut my rain barrel because it was very tall for my yard...I used the top of the barrel (with the top lid attached) as my pool. I can drain it with little effort now by putting a small aquarium siphon in the pool and letting it drain into the garden 2 feet away. But I will be making it easier... I will be raising the pool on some bricks and putting a pvc elbow and a shut off valve under the pool coming out of the pre-screwed (1.5 inch hole) spout on the lid of the rainbarrel...then attaching a hose to the pvc pipe and then I don't even have to use an aquarium siphon, just turn a valve and start watering... it took a while to get the ducks and their yard right, but I'm definately glad I have gotten to this point.