No.
There is only one Constitutional path when there is no clear winner via Electoral College and Electoral votes accepted and certified by the President of the Senate (Pence).
Put aside the fact this would have been a 'fake' case of no clear winner as the Constitution never contemplated fraud in the process, but had Pence gone along with the fraud and no certifying of the Electoral College happened in the Senate, the Constitution then requires it move to what is known as a
Contingent Election .
The House makeup (only the House votes) had the GOP with the majority of seats based on how they are counted in a Contingent Election, meaning if the GOP with a majority vote could have put back in Trump as POTUS.
Some people say 'The Supreme Court would never allow that'. By the Constitution the SC actually has no role here via Separation of Powers. Once the States complete their certifications and submit them then elections are run by the President of the Senate by counting and certifying the election by the required date, OR, throwing it to a Contingent Election, if he cannot do it due to real issues.
So even if the Dems got the SC to hear it, the SC could either say, 'this is not our role, this has to be done thru the VP or House', or like they did in Gore V Bush, they can offer a ruling that many Constitutional experts said back then was really just an opinion, as they have no role.
So lets say the SC said to Trump and House Republicans 'that was wrong, Pence should have certified those votes', do we think Trump and House GOP stand down and just hand it over or do they tell the SC to stay out, as they have no Constitutional role?? I know which i would bet on, thus driving the country into a massive Constitutional crisis.
BTW there were some arguing for AL Gore to not accept the SC ruling, as President of the Senate, and someone who was shown after in many recounts to have actually won the election versus Bush. But Gore commented on that, and that if he refused it would tear the country apart so he was stepping down, even though he did not agree. He die not have to.