Soulburst & Plasma Grenades

Can a Soulburst "assault" in either the movement or shooting phase by-pass the initiative penalty for assaulting through cover?

I tend to think this won't work... but I'm not 100% sure. And it would be nice to have Incubi at initiative on the first turn.

Also, I noticed that Yvraine doesn't have plasma grenades, so I was hoping there was some way around that.

No. Nothing about it gives you permission to do so. You charged as if it was you're assault phase. If you infracted that penalty it happened.

So do you have to go through a full charge and fight sub phase for other initiative to go back up?

No. You need to go through an "end of turn". The rules related to the initiative drop have to do with the turn in which you charged. You could in theory Kill a unit, trigger a soulburst and charge another unit at I1 but not hold a fight subphase because you soulburst at I1. Next player turn you'd strike at initiative but not get any bonus' because you didn't charge that turn.

Makes sense. Cool. Thanks.