Fire Emblem: The Sacred Stones, Super Trainee Question

So, I'm currently playing through Sacred Stones and I have a question regarding the Super Trainee classes. I know that you unlock them by beating both Ephraim and Eirika's campaigns. Everywhere says that you'll get to use them in your third playthrough. But since I've found no source directly answering my question, I figured I'd post it here, anyways:

Would this work?

1. Beat the game as Eirika

2. Beat the game as Ephraim

3. Launch my completed Eirika game and level a trainee to 10 and get the stage 2 trainee promotion.

Any help on this would be great, if I'll have to restart to use them, then I won't have to be nearly as careful in my current run.