If there are no cities on the board, barbarian strength is rated at zero. So automatically the players have tied or beaten the barbarians. Are progress cards allocated under these circumstances? If there are activated knights on the board, can a victory point be achieved?
This is answered by the online Catan FAQ.
Can the players win against the barbarians if there is not one single city on Catan?
but that's if you're playing the English variant. In that variant, each player chooses how much to contribute to the defense of Catan. A player isn't allowed to defend Catan if they have no cities, thus no-one can win and get a reward.