It would be hyper until all other weapons got overdrive, which is the ideal scenario (and I’m pretty sure that’s the plan, eventually at least). Actually, it’s the only scenario, because weapons without it would be heavily handicapped.
Hypergun just needs to work. This means giving it a damage boost on mid power and increasing its overheat time. Mix that in with a DPS reduction on low power and you’ll have a pretty well balanced gun. (cough)
If this kind of limitation does make it into the game (as it should), it will likely be dependant on the reactor, and so the exact duration/cooldown will vary.