Yes, it will stay on the device. The reason I recommend keeping a backup is in the very rare case something goes wonky with your tune after they run the inspection. I had this happen one time out of many inspections and I wished I had a backup. Even reflashing with the tuner device didn't help. AM ended up helping me out giving me an updated set of tunes.
Super rare and possibly other factors (too many to fully say this was the exact reason) but just do it as a piece of mind.