The Houses of Congress have the constitutional power to decide on the qualifications of any prospective member. See Article I, Section 5 paragraph 1.
Ol’ Rollie will probably win the battle of getting the seat, but the Senate will win the war by shunning him for the duration of his term. He will not gain any power or support, nor will he receive any assignments other than those mandated by law, and then they will be at the bottom of the priority list.