You could, but in that case, whats stopping you from just sticking a regular 9V in the guitar in place of the battery being charged? You'd also have to leave your guitar plugged in and the amp turned on for a long time before its charged (guitar signal has a tiny voltage) and that could be bad for the amp. Its technically possible, but I just don't think that its worth it.
Also, question to anyone who is skilled in wiring:
In the case of my diagram, a stereo cable is ran from the power pedal to the guitar to provide electricity. Am I correct in saying that a mono cable ran from the guitar to the pedalboard or amp bypassing the power pedal would allow the guitar to function normally as passive opposed to active?
I don't mean to threadjack if that how I came off as, I'm just trying to contribute