I hadn't considered the potential time travel aspect before, but I think you may be right. Previously, I'd assumed that the Gibbs had some kind of built-in immunity to whatever had wiped out most of the population, be it a chemical attack or superflu of some kind, and were now wandering the planet as potential saviors/warrior-kings.
In any case, they do appear to be scouring the city for survivors or supplies of some kind, so perhaps even the Bee Gees don't yet know what has killed everybody else. The line in the song about "the New York Times' effect on man" foreshadows a moment where they find out what went down on Earth via an old newspaper. And the shot of the three of them sitting in the train towards the end implies that they get the train working again to escape the city, almost certainly on the run from mutant scavangers. But that leaves open the question of who's driving the train. Andy Gibb?
No, it's Frampton. Has to be Frampton.