I think it would be plenty, but probably not overkill for such a large fuge (assuming you want to grow algae aggressively, and not just keep it alive).
24x24x18 is actually closer to 45gal in space, so I assume when you say appox 20 gal, you mean your not going to be filled the entire level?
I personally would get the A160WE Tuna Sun...it's just a tiny bit more expensive, and just a bit more powerful.