I don’t think so. The Supreme Court does not hear evidence, only arguments of law. If the campaign tried to introduce new evidence, SCOTUS could send it back to a lower court. Appeals are generally limited to arguments about procedural errors or incorrect application of the law.
This belief in some quarters that the Trump campaign’s lawyers are sitting on a pile of damning evidence and only waiting until it’s in the Supreme Court to show it is absurd.
Worth repeating.