As other people seem to be taking this seriously, I have to point out
that you have missed the need to control the generated supply voltage.
Without control, VCC will just increase until it blows up the AVR or
some arbitrary limiting factor comes into play. Perhaps you think
that you have a voltage doubler here. This is not so. A boost
converter requires feedback from the generated voltage to control the
switching mark/space ratio in order to produce the desired output.
I thought either predetermined mark/space ratio could do (with known
power consumption) or the AVR could somehow use the A/D circuitry to
deduce the Vcc and act accordingly (thought I am not sure this could
be done without more external parts).
If it has an internal band gap reference like the ATmegas, then just
measure this and you can calculate