It’s very unlikely that SCOTUS would accept the case. They have refused to do so in several similar cases, including the NJ senate race where the Democrats cheated in 2000 and the recent race in Alaska where Murkowski supporters cheated.
I think it all boils down to this: What does the Chicago Mafia want? It seems unlikely that the appellate court would have found against Rahm unless Daley and the Machine approved. And although Obama says he supports Rahm, some have their doubts.
Well, it’s up to the Illinois Supreme Court, IMHO.
Extremely unlikely the Supreme Court would intervene - the cases cited above, arguably, have a federal component since they decided a member of Congress. The election of the major of Chicago has no federal component (well, except when Daley stuffed the ballot boxes for Kennedy - but that's pretty remote.)