It probably would not stop it from starting, as the power generated is dependent on the alternator speed (at least within reason). For a traditional non-inverter portable generator, it would probably just take a longer time to get up to speed and the engine would be somewhat harder to crank. I don't think most of them have a lockout or time delay circuit.
An inverter generator probably wouldn't start powering the load until the engine is at least mostly running, and it might well kick out immediately. Incandescent lights have a pretty significant startup current surge for the first fraction of a second when they're started at full voltage. That's why light bulbs almost always burn out with a flash when you first turn them on.
As everybody else said, it's not a good idea to start a generator under load regardless.