Answer:
No, mileage is usually calculated either by a trip computer (if so equipped) or manually by dividing the number of miles traveled, as indicated on the trip meter, by the amount of fuel put into your car when it is refueled. The fuel gauge is only an indicator of how much fuel is in the tank.
By the same token, if you knew how much your car got per...let's say, quarter tank, you could figure out how many miles you can squeeze out of your tank without a trip computer. However, this method is less accurate, because most fuel gauges do not provide a precise readout (i.e. there are no indicators of the actual amount of fuel remaining) and they do not travel from "Full" to "Empty" at a constant rate.