Yeah it does. You just haven't noticed. The foot flexes when you push it against the pedal. If you ride with a good stiff sole, you'll notice the difference immediately. After that, when you ride in street shoes, your power transfer feels "mushy".

But wait: this goes for pedaling on the ball of the foot, like in toe clips. If you ride unsecured, with the pedal in the arch of your foot, there's probably less flex; fewer joints in the line. Don't know how much a stiff shoe improves power transfer in that case.