Considering he can phase through a Rasengan which, like Susanoo, is made of chakra, I bet he can get through Susanoo. But by that point you probably couldn't see him, seeing as he'd be completely in Kamui's dimension. So I don't think he could grab the user.
@Actionmanrandell, Obito doesn't phase through barriers, he teleports completely into the Kamui dimension then comes out on the other side.
Also, if he was phasing through Susanoo he couldn't absorb anything into Kamui's dimension since he can't use both powers at once. I'm not sure what would happen if he tried to touch Susanoo to absorb it anyways, it might just harm him on contact.
Can obito go through complete susanoo to grab the user? Wiki says user can decide who enters and exit susanoo. (Please no gaara reference)
he can go "through" susanoo but he cant grab the user because he wont be really "phasing" like in the real sense... it is more like partial teleportation, and unfortunatly he cant manifest himself in something already existing...
A Kamui user can phase through Susanoo, he might be able to even appear inside depending on what Susanoo we are talking about.
If we are going with Complete Susanoo, that is waist and no leg, then the user can appear inside as if the Susanoo user allowed him, giving him the chance to strike. Anything else from that, a full body Susanoo would be hard, due to it having leg or being a full body complete armor tailed beast powerful Susanoo