NO your transmitter (radio) does not have to be on the same channel. If you get a Futaba the student radio isn't even turned on. I don't know about the latest JR's but in the past they had to both be on, seemed stupid to me but then I don't like ford's either.
Also you don't need the antenna up on the student radio. As said before, find out what your instructor uses and go with that system or find a different instructor with the radio YOU like. ENJOY !!! RED