^^^^
Just to be clear, my house internet will be backed up but the Gateway will be mounted on an outbuilding that is too far from my house to receive WiFi. I have an access point in the outbuilding but the outbuilding is on separate feed conductors that won't be backed up.
I did finally manage to talk to someone at Tesla about my technical question. He thinks they should be able to move the branch circuit that currently powers the access point to the generation sub-panel that will be mounted on the outbuilding but he wasn't sure. Something about having a load coming out of a generation panel.