The engine will burn the same amount, but with the gen set taking fuel out of the same tank, it will take more to fill up.
If you're getting 10 mpg running at 60 mph, as example, and running the gen set at the same time, using 1 gal per hour, in that hour the engine will use 6 gallons, the gen set one, for a total of 7. If you don't account for the fuel the gen set has used and try to calculate fuel mileage simply by the amount it took to fill the tank, compared with the miles on the odometer, you'll get something like 8.6 mpg rather than the true rate of 10 mpg.
Make any sense?