When a generator is off, it’s off.  It won’t cost a cent and it won’t consume any fuel, regardless of the fuel curve.

When a generator is on, HOMER will calculate its fuel consumption from the fuel curve.  If a generator is actually idling and generating zero kW, then its fuel consumption will be equal to the no-load fuel consumption.  That would be a very rare event; the minimum load ratio would have to be zero, and HOMER would have to decide to run the generator just to supply operating reserve.  But the no-load fuel consumption is still important to HOMER, because it factors into the fixed generation cost.