Certainly not a generator, at least not unless there was some miracle fuel cell fuel. The "electric boost" would need to be completely idle most of the flight (which creates some interesting challenges regarding conversion of electric torque to air movement).
Oh, that's sobering. All the referenced modeling seems to start with hypothetical batteries many times lighter than we have, and even then they only give minor emissions reduction hardly beyond what we are used to from e.g. succeeding generations of 737. And only under the assumption that the electricity used is completely emission-free.
And why even bother modeling constant power split? You might just as well linearly interpolate between conventional and an all-electric design and call it a day. Everything interesting about hybrid propulsion happens when the ratio is varied with power demand.
What's interesting is how much mass they account on the electric side in addition to the battery. This kind of validates H3X.