Yes they can. Look at Hawaii in the 1960 Election.
Ironically, Richard Nixon was not only one of the two candidates in the 1960 election ... he was also the sitting VP presiding over the joint session of Congress in January 1961. By the time that joint session was held, the final recount in Hawaii had established Kennedy as the winner. Nixon could have legitimately accepted both sets of disputed electors and had Congress vote on them, but he decided it wasn't even worth pursuing.