If it was 'just' a switching supply with NO input power-factor compensation then yes 80Hz would work fine but it will not increase power per-se, the PSU just pulls lower current and it will certainly not increase power out of the PSU because that is set by the regulator(s) in the PSU.
That said, for the past oh, 10 years or so in the interest of increasing PSU efficiency and even more importantly greatly reduce/virtually eliminate the high power-factor that any capacitor input load presents to the power line all PSU's that can deliver more than 500W are required to use PFC (Power Factor Control) circuits and those are very sensitive to frequency. Go outside the 50-60Hz design parameters and yes, the Majik Smoke will escape...
I should add that one cannot just 'goose the throttle'... yeah you could fiddle with the carburetor to speed up the engine but - at a bare minimum the genset has a mechanical speed governor and most likely an electronic one you'd have to hack. Then there the circuits that regulate the voltage out of the genset. Bet they won't like it...