The only difference between John Roberts and Sam Alito is that one of them openly supported the January 6 insurrection, and the other one was quietly hoping for its success ballsandstrikes.org/scotus/trump...
I don't think there's a clear answer in the opinion. Maybe no, because that isn't part of his Article II duties; maybe yes, because ensuring election integrity and managing the relationships between the federal government and states is part of his job. The opinion is squishy on this, on purpose.