Possibly, but why? He has to learn everything there is to know about being on the supreme court (including things like where to park in DC), and all the other work he is expected to do. All this to weigh in on a case that was 7-1 (and the 1 was a minor dissident), so his voice would mean nothing to the result, and it would inflame the Democrats (in this case - if a Democrat did the nomination the Republicans would be inflamed) who would look extra hard for a reason to impeach him. If congress is close such a thing along might be enough to impeach.
If this ever happens it will probably be a 4-4 decision where the other justices - knowing they are tied - ask for a tie breaker. Expect there to be a lot of publicity: they will want to make it clear to everything that everything is being done right. This probably includes redoing the oral hearings for the benefit of the new member.
