I would assume the only reason you can make power pulling up is because of the strength and power you are using from your arms/handlebars. Basically when you pull up while pedaling the bike has less weight on it, therefore less heavy in general. You're not actually producing more power, it is just being utilized better.
For example, if you built a bike into a drag bicycle and had to pull an object behind you. You could pull it faster by pulling up on the bike however, you would not be able to pull more weight.