With the new Wireless Trainer system if a 12 fga radio was the teacher and a 10c was the student.
Would the channels on the 12fga have to be changed to match the 10c Like it does now with the normal training cord?

When you set up any trainer system, you have to be sure that the student and instructor transmitters have the same channel setups. It makes no difference whether the connection is a wireless system or a trainer cord.