Perhaps. The Senate has the right to expel a member of the Senate but whether they can refuse to seat a legally appointed new member is open to question. The argument rests on two parts of the Constitution.
Article One, Section 5 of the United States Constitution states that "Each house [Senate or House of Representatives] shall be the judge of elections, returns and qualifications of its own members . . ." In addition, "Each house may expel a member." During its entire history, the Senate has expelled 15 members. But these were members who were already part of the Senate.
The 17th amendment to the Constitution states :"When vacancies happen in the representation of any State in the Senate, the executive authority of such State shall issue writs of election to fill such vacancies." In other words, the governor shall appoint a successor when a vacancy occurs.
Refusing to seat a new,duly appointed Senator may only be possible if the Senate has some indication that his appointment was corrupt. Since they have no such knowledge that Burris' appointment was corrupt, many constitutional experts say that to refuse to seat him would deny the citizens of Illinois proper representation in Congress. According to ABC news," . . election law attorneys said that senators may not have the constitutional power to refuse to admit Burris into the Senate without some indication that his appointment was corrupt." Thus, it is unclear what will happen if Burris attempts to take his seat.