Pulling up on the pedal with any force would likely be problematic for folks like myself. When I consciously really try to pull up on the pedal, I can feel the pull on my groin muscles, and not in any sort of good way! They're tiny untrained muscles, who's job is stabilization rather than power output, I think, in normal folks like me.

Still, just lifting the weight off the pedal on the upstroke is bound to improve one's pedaling efficiency, since the leg doing the downstroke is just putting it's power to use propelling the bike, and not in lifting the dead weight of your other leg!

The soft shoe vs. hard shoe argument is likely too complex to be dealt with by simple theories, and would need experimental data, since the involved problems of elastic vs plastic deformation and hysteresis loss would probably be "non-trivial", and different for different styles of shoe. Running shoes would be bad, since they're designed to absorb shock, and as such, would be "lossy", but the way one is pedaling would likely make a difference, with low impact "spinning" suffering no significant difference in energy loss, while a more "mashing" power pedaling might, maybe possibly but unverifiably without experimental proof, suffer a noticeable loss of performance.

Mind you, my first and third paragraphs are just me, talking out of my... alternative orifice. The second paragraph and this one, are the only two I can claim to be unbiasedly factual!