It seems attractive, but the problem is the keel. A sailboat has a keel that keeps it from slipping sideways in the water: it can only travel forward. So a sailboat can travel at an angle to the wind because of the force on the sail, and the force (in a different direction) of the water on the keel.
If your sail and your keel are both in the water, the same current will push on both, and it won't work.
It seems all of the problems stem from the boat being in the current. If the boat could put down anchor to stay stationary for awhile, charge up some batteries, and then motor upstream, it would work fine. Without some stationary attachment, though (an anchor, a rope to shore, etc), I just don't see a way to make it work.