I agree, the short answer is no. It will take longer than an hour, probably quite a bit longer.
How long it takes depends partly on your converter. If you have the original circa 1988 converter, it probably is a single stage unit and takes somewhere between half a day and a day to come close to fully charging the house battery (though you could get some useful charge in a few hours). Replacing it with e.g. a PD 9200 series converter would help a lot; you could get somewhat near a full charge in a couple or few hours. If you have space, replacing the single marine/RV battery with e.g. a pair of 6V golf cart batteries would increase your usable battery capacity quite a bit and reduce the total amount of generator runtime required.
As a general rule, the last little bit of battery charging takes a lot longer than the first portion. Going from, say, 50% charge to 80% charge is generally a lot quicker than going from 80% to 95%. Even under ideal conditions it's not really practical to charge a lead-acid battery from 50% to 100% or close to that in an hour (for the sorts of batteries generally used in RVs, at least.)
The generator probably uses closer to half a gallon of gas an hour when lightly loaded, by the way.
If you have a good battery combiner setup, you could also use the main engine to charge the battery, and there's at least a reasonable chance it could be quicker as the alternator output voltage is higher than the converter output voltage, and hence the charge amps would be higher. To really know what's going on in any of these situations you'd have to measure the voltage and battery charge current, or have some fancier meter like a Trimetric that measures them and does some figuring for you to suss out the state of charge.
