I would let it. The statement in the many shot feat does not apply to this. With MS, it's against a single target. Eldrich chain bounces from target to target. And since the eldrich damage is halved each target after the first, it will even out. Plus, he took a dive in warlock power to multiclass, so its more than likely not as bad as it would seem.
To use improved invisibility as an invocation, the PC would need to have 16 lvs in warlock. That does not leave that much space for rogue.
If he is useing a wand to get that effect, than he is spending enough resources to justify letting him do it.