You most likely have a two stage system. That just means you have two different regulators. First stage is a high pressure regulator at the tank. It will most likely be red. Don't let "high pressure" fool you, it is only 10 psi. Where the gas line goes in your basement you should find another regulator, about twice as large as the one at the tank, and most likely painted brown. This is your second stage and it reduces the pressure from 10 psi to 11" w.c. The btu capacity of this regulator will determine if it can supply your current inhouse loads + the generator. The common regulator used is rated at 935,000 btu. So add up the current loads in the house and add the expected generator load to see if you need to add a regulator or not.
Just for reference my loads are: Central heat, 90,000, tankless water heater, 157,000, kitchen stove (estimated) 40,000, generator, 203,000, 490,000 total. That would leave 445,000 btu on one regulator
Even if the regulator has the capacity, your existing basement pipe could be too small. You could get around that by supplying the generator with a new pipe from where it comes into the basement, instead of at the gas cooktop.
I attached a gas line size chart. I have a more detailed size chart, but it is too big to upload. It has info on calculating losses for 90* elbows. If you need it, pm me. Or just google for gas line size charts.
You can see from this chart, that at 65" and a 203,000 btu generator, you are close to maxing out 3/4" pipe. If you need many elbows, 1" pipe may be needed.
jp