When the rider flexes the frame the whole system acts as a spring right from the tires to the wheels into the forks and frame and even the seat post and handlebars. Some of the parts, such as the tires and tubes, will have more damping (the hysterisis that LarDasse mentioned a couple of posts up) and some parts less. This energy will return into the system or be converted to heat as already mentioned. And since we don't see the frame and wheels glowing red hot it stands to reason that much of this stored energy goes back into pushing the bike forward. There won't be an easily resolved vector path of forces that show the side flex to wheel drive because the combination of forces through the wheels, cranks, fork, frame and rider's body are a convoluted mess. But the final resolution of all the pulling and tugging will be something that aids the rider. If it didn't then we would be choosing our frames, cranks, bars and wheels based far more on how rigid they are. But as we've seen here that is not the case. Flexy Fliers can do as well in racing as Rigid Racks.