Apparent power (what gets added due to a poor power factor) does impose some load on the generation and especially distribution of power, but electric utilities only meter actual power for residential customers; you don't have to pay extra for a poor power factor. Put another way, a standard residential electric meter is measuring and you're being charged only for the actual power, not for the apparent power.
The extra gas being consumed by the generator is not going into powering the converter (the converter isn't using any more electrical energy), but rather into losses in the generator itself due to it having a less ideal load attached to it. No doubt that gas and so forth is of interest to a generator operator, but less interest if you're buying utility power and the power company doesn't charge you for it.