So I put Piper in a set of Power Armour with a fusion core that had almost ran out just to watch her get kicked out mid-battle to see what happens... and she never did. We finished the battle (and she busted up the armour... grrr) but when I kicked her out of the armour IT STILL HAD THE SAME AMOUNT OF POWER AS WHEN I PUT IT INTO THE SUIT.
So not only do companions have infinite ammo for their invisible weapon (as in not in the inventory) but they also have eternal fusion cores.
Another thing happened for the first time during that battle. She picked up a Synth's rifle and was using it for most of the time... no ammo for it but she was still using it. Yet if I give her a gun I have to supply the ammo too? I have noooooo clue to the rules here.