If i had more time i could look at the issue more closely, however at this stage i am tied up. This problem has to be looked at meticulously. There are many variables which could cause a problem.
First as you say, you need an air exchange system, not only for your plants but the generator itself. Fumes need to be vented and fresh air replaced for oxygen.
You will also need to find the right generator, just any old generator might cause problems. Not all generators are made to run long hours. A backup generator may not last long and could break down. Primary generators are made to run continuously.
There is also the efficiency problem, last i checked generators are not as cost effective compared to residential electricity. You would be likely spending several hundreds of dollars PER MONTH! on fuel. But exactly how much depends on your cost per gallon where you live and the efficiency of generator chosen. Have a look as some generators out there and calculate the cost based on its fuel efficiency.
The quality of the output power may be a problem as well, though if you using LED this would likely not be as they have regulators and filters that do a could job of providing clean power to the lighting fixture.
The list goes on, Oil checks, Spills, Noise, time. At the end of the day, it would very likely be cheaper to buy weed than to grow it this way.'
In the next few days if you want me to look at it more closely i can.