Unless I missed it, at no point did he officially leave, just strop of in a sulk. But it's likely I just missed it.
He grabbed his things and left, he was no longer wearing the DIK jacket after that. He likely applied to a dorm too, or is staying somewhere in the city until he can get into a dorm.
Nick's no longer part of the frat. He grabbed most of his things and left, it's not likely that he's going to be coming back with all of the shit he said: he snitched on everyone with the secrets that they kept. He broke any trust he had. And even if by some chance he wanted to come back, at LEAST half of the DIKs will say no given what he did.
Nick even said that he should've quit just like Vinny did back then, but he didn't have the balls to do it. So yeah...it all leads to him being out of the DIKs.