> If the TX were running at full power ... Leave your phone in a metal, security cubby and your battery will die quickly

If the phone can't hear a network (not just faint signal like airplanes on certain heights), would it actually transmit?

I think the battery drain would be from active RX searching for networks instead of sleeping. You get a similar though probably lower effect, when in roaming without setting a fixed network - an idle phone without crapware will burn way more energy.