I'll openly admit that I do not know the actual answer, but I can tell you this - all EVs have an on-board 12V battery to power the normal vehicle stuff (lights, screens, computers etc), and they have a DC-DC inverter to charge the 12V system off the main EV battery. This charging function only occurs when the vehicle is powered and ready to drive - it is not active all the time - so it only happens in "key-on" kind of situations. The big question is whether or not that inverter can put out the power that the PCP compressor will draw so that it does not over discharge the 12V battery (the inverter does not have to have the same kind of output as a regular alternator as there are not big drains like starter motors and the like). I don't know what any particular Tesla is rated at in this regard.
I would think a short run in "key on" mode would not be a problem, but it would be best to know for sure. EVs use contactors powered by the 12V system to "turn on", so if the 12V system loses power, the vehicle won't be able to be "started" again after the power is turned off. They need the 12V to run.