Steph,
I am sure it's possible, but the problem is that most of the "check" valves that you describe are gravity driven. I would think that if the tank would fill that the trap door in the check valve might not seat properly and "float" more or less depending on where it could be installed given the space limitations. See if the tank fills and you by mistake use the shower, the check valve would open and then might not close and since you couldn't empty the tank in the senario I described in my last post.
A nice idea, but not sure how effective it might be. Of course, I'm no engineer. But I like how your thinking though!
Eric