> That being said, I wouldn't be surprised if they didn't start the generators during critical phases so they may end up using some fuel for a flight, but not much.

I would guess the opposite. Many parts in a turbine engine are "lifetime limited" by number of engine starts. That is, you are required to tear down the engine and replace certain parts after a certain number of engine cycles.

That makes the economics of the turbine hybrid radically different if you need to start it every time you land vs. only the rare cases where you need to dip into fuel reserves.

For example, the PT6A (a common 500-1000hp turboprop) requires the turbine and compressor disks to be replaced every 16,000 cycles. That's about 5 years of commercial service at 4x round trips per day. But if you only start the engine once in every 10 flights, now those components (theoretically) last for 50 years of flying.