Crank length and power

My understanding is that setting the crank length on a head unit sends an update to the pedal and the pedal uses this to calculate what power is being output. Is this correct?

If I then move the pedals to a bike with different length cranks the power recorded by the head unit will be incorrect. 
I have tested this using 2 head units. My 1000 and my 130. One says 175 cranks, the other 165. The recorded power for a ride is the same. This leads me to believe that and processing as dar as the power number goes occurs in the pedal, using the last set crank length.