Depends.
Gas engines are typically most efficient - in terms of kinetic energy delivered per volume of fuel consumed - when sized so that they're running near maximum load.
Unfortunately, it appears you must upsize the generator to handle the draw. The EU2000i would probably be fine for the 2012 1 kW charger or a 2013 650 W charger, but perhaps not the 2013 1.3 kW charger.
For example: Honda EU2000i
claims a full 0.95 gallon tank will deliver 4 hours of runtime @ 100% (1600W) = 6.7 kWh delivered/gallon, 9.6 hours runtime @ 25% (400W) = 4.0 kWh delivered/gallon.
1 kW would be around 60% load, 650W would be around 35% load. Figure 4.5 kWh/gal @ 35%, 5.5 kWh/gal @ 60%.
Trikester sees around 70 Wh/mile on his trail rides. If he charged off of a EU2000i then he would see the equivalent of around 64 mpg. He's probably doing better than most small gas bikes in low speed trail rides.
I see around 120 Wh/mile at the wall in my mixed riding. If I charged off of an EU2000i then I would see the equivalent of around 46 mpg. I would expect to see 60-70 mpg in mixed riding on a 250cc gas bike.
Suppose a 2013 S could charge @ 1.3 kW (say 6.5 kWh/gal) from the Honda generator. On the highway, they see 140 Wh/mile @ the battery, or probably 165 Wh/mile at the wall. They're getting the equivalent of 40 mpg. A 500cc gas bike would probably see 50-60 mpg.
Using a generator to charge the Zero is something much like a true serial hybrid, like the Volt in one of its two modes of operation. This has some significant inefficiencies - converting kinetic energy to DC, charging the battery, discharging the battery, converting to AC, converting back to kinetic energy. So it's only more efficient when those inefficiencies are overcome by allowing the gas engine to operate in its most efficient regime of operation, or by introducing other system efficiencies (kinetic energy recovery via operating the motor as a generator, reducing aero drag, etc).
Trikester's trail riding is a great example. The gas equivalent would be operating at very low load most of the time, spending a great deal of time idling. A 250cc gas bike would probably not do terribly well here. If the gas generator was sized so that it was delivering 6.7 kWh/gal then he would be seeing nearly 96 mpg.
Highway riding is the flip side - it's relatively constant operation and the load is moderately high. Gas bikes are fairly efficient on the highway, relative to low speed operation.