probably but that she doesnt have any dirct relationship with anyone from the gotei 13.But is very fond of ichigo. so she may ally with him
She's unlikely to move permanently to either Soul Society or the Living World so the point is moot. If you are asking if the Gotei 13 would object if she joined their side to fight against Aizen and her old Arrancar comrades, the answer is no. The Shinigami have to date not shown reluctance accepting help in their fight against Aizen and his Arrancar.