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I've been experimenting with Teachers, and I'll share what I've learned.
So far, what I've done is put a Teacher (only one I have is level 24) into a level 0 item and then clear the first 10 levels, subduing innocents as I go. (Not using Gency's because they're mostly crappy items I don't intend to max out anyway.) When I leave through Innocent Town, the innocents have roughly doubled in effectiveness. (It's hard to tell exactly because my TV sucks and the numbers are blurry.) I can combine the boosted innocents with other subduied and boosted innocents of the same kind, and they remain boosted. If I combine them with unruly innocents, they go back to their normal, non-boosted strength. Not sure what happens if I combine them with subdued innocents who haven't been boosted by a teacher.