OTOH, I tried measuring how much energy could possibly go into the frame.
I sat on my bike with the front break applied, shifted my weight from the saddle to the pedal in 3 o'clock position and measured the vertical pedal deflection, which came out to be 3-5mm with me weighing 69kg. Assuming that all my weight pushes the pedal it makes it roughly 1.4J of energy. This transfer happens twice per revolution and with 120rpm cadence we get 5.6Wt going through the frame. That might seem like a lot at first, but pushing with 700N at 120rpm is _A_LOT_ of power. Even if I inefficiently push the pedal straight down, I get 4*0.34*700 = 950Wt of power. And 5.6Wt/950Wt = 0.6%. Not that much.

PS. all measurements done on a steel frame from Columbus SL