We have that style twist lock in our training center for 3 phase 240. I would check with the generator manufacturer and see what they have to say. I wonder what they would say about pulling from 2 legs to get single phase (unbalanced load). I would also want to know how much I would need to de-rate the generator output.
This would also tell you if the generator had breakers on each leg and thus if you needed to add one. My suspicion is that they are usually built in.
So in essence I have said a lot to tell you nothing.

I must be a lawyer or something...