Quick question about downgrading to an earlier iOS version

Im currently at the Genius Bar and might possibly be given a new iPhone for a hardware issue I have. Problem is, its bound to have the latest update.

Ive never updated my current OS past 6.1. Would I be able to restore from iTunes and downgrade from 6.1.4 if the phone were to get replaced? If not, I might just pass on getting the phone replaced. The tethering app I use from Cydia is way too important for work.