Depends on your converter size.
a 45A converter can draw upwards of 700W at full load (depleted battery plus any 12V items running).
I have a 60A converter and it is rated as 1000W draw.
With that said, as long as you are not planning to run a microwave, A/C, hair dryer, toaster oven or any other high wattage item you could possibly get away with 1000W gen.
However do keep in mind the gen rating often given is the SURGE rating. So, a 1000W advertised gen most likely will have a CONTINUOUS RUN rating of 800W which might be a bit light with a 45A converter..
The noise police should be along shortly.. But a $100 gen is not going to be something you are going to want to run near others and it is a hot button with avid boondockers..
Something else consider, if it a new $100 gen and is 1000W it my be a two cycle engine (like a weedeater or chain saw) and will require mixing two cycle oil with the gas..