I'm skeptical. When you're up out of the pedals and sprinting on a bike, you are transmitting an awful lot of energy. I don't quite see being able to push quite so hard when sat down.
One way of thinking about it is that work is force times distance, so if you aren't moving WRT the bike, and push just as far work goes by force. Assuming you don't have toe clips and so aren't pulling up with one foot while you push down with the other, then at most you can push down with your body weight. (You could push harder but that would leave your body accelerating up at the end of the stroke.)
You're thinking about it from a physics point of view, which is kind of abstract, and possibly not considering all the movement involved. I'm thinking about it from the point of sprinting for the finish line at a race last Sunday. I really don't think I could have brought the same force to bear while sitting down.
Also: modern bikes have clipless pedals, not toe clips.
