Not exactly. The phone needs to transmit with enough power to communicate with the tower. When connected to the tower, the tower is constantly monitoring the signal and sending back information to the cell phone to tell it how much power it needs (without using more than it needs and wasting battery life).

If a phone isn’t connecting to any towers (like on a plane) it assumes it is out of range and is blasting out max power trying to find something to connect to. During hurricanes, many towers are down, which can overburden adjacent towers as well (since each tower only has a certain number of slots/channels it can handle). It means that you may not be able to communicate with your closest tower, since it is down, but you also may not be able to communicate with the next nearest tower, since it at capacity for current users, which puts you in a longer distance higher transmit power situation.

From what I have heard, those Stingrays act as fake towers, so I would assume they could set them to always tell the phones it needs max transmit power.