It's doable, but I would question why? I wouldn't add another cell to the trainer if it were me. I would just get a nice 1500 mah 4 cell battery. It will weigh about the same as the battery you already have, so there should be no balancing issues. make sure you get a AA cell battery pack, and not a C or sub C battery pack for weight issues.
For the tx, same thingget yourself a 1500 or larger battery pack. The tx upgrade will be one of the single best investments you make, as it will allow you to fly all day without recharging the radio.