Not an engineer - don't play one on TV, but I'm pretty sure a generator cannot keep up with the battery usage needed to drive down the road.
Meaning as the battery gets depleted, the generator will start charging it back up, but the power going in will in no way match what is going out, but it will extend the milage.
So you will never be able to go out with an empty battery and a full tank of gas and expect the car to move.
Plus that two way flow of electricity in and out of the battery, will generate a lot of heat, which will have to be handled with some cooling, which will also deplete resources.
I'm also thinking, this type of usage will shorten the battery life.
Anyway, this is my understanding, unless someone has 'built the better mousetrap' and my knowledge is outdated, which is possible.
Check out the work that Eddison Motors is doing. Same concept but in a semi. They say that they will be extending the battery life because the generator will always keep the battery between 20% and 80% charge. That being said, it will be interesting to see the specs of the scout engine generator combo once they release that. I am REALLY hoping it is big enough that you would only have to stop for gas if you wanted to.