If log_2(num_players) > num_rounds, then there can be two undefeated players.
Yeah this is not an issue. Swiss tourneys on Challonge (and in general) always run at minimum the number of rounds to have 1 undefeated player. I guess with intentional draws in some tournaments 2 players can have the same record. But there are a bunch of different tiebreaks in that case anyway.