You would be correct about
You would be correct about reducing weight when comparing "a small gas turbine APU" versus a diesel engine. However, my point is that whatever you use to turn the generator, the generator by itself (without batteries) should be sufficient enough to power the vehicle down the road. This would eliminate the "extra" weight caused by batteries.
Now whether this setup would increase, decrease, or remain the same regarding overall fuel economy is a matter that I don't know the answer to. "CSX trains, on average, can move a ton of freight nearly 500 miles on a gallon of fuel, based on they're 2015 revenue ton miles and 2015 fuel use." That's impressive and I'd like to know why that technology has not been adopted by the automobile industry.