Engine used in Prius has to be affordable. They have 250h for step up effort. So definitely do not expect any kind of supercharging or anything that will significantly get the price up. Yes, they can increase battery output by increasing the battery size, and maybe even D4S to increase engine power but that is the max. Of course other than improvements that new engine will bring with itself.
Prius is not meant to be a cost-minization vehicle. It's a partial technology demonstrator and it has been the way since 1997. If they cared so much about reducing cost they wouldn't put aero wheels, carbon fibre hatch, bioplastics interior and whatnot. The Prius doesn't benefit at all from a rear disc brake yet they do it for the sake of weight reduction (when their mainstream truck carries drums in the rear).
If the 5th-gen Prius debut with the 250h powertrain. What would distinguish it at all from a Corolla hybrid? A Corolla hybrid will be more comfortable, more practical, and cheaper. But the Prius is all about efficiency maximization, a demonstration of Toyota's technology prowess. The Prius is already outshined by BEVs and FCVs, so it absolutely needs some bragging rights to remain relevant, like a 45% ICE, preferably beating SkyActiv-X.
The only scenario I see Prius not needing a 45% ICE is if they use a significantly bigger battery like the BMW i3, basically turning it into a strict EREV. But then it is just diverting the cost to bigger and heavier batteries.
As to the electric supercharger... if they power SC with batteries, then how much is left for electric motors to drive the wheels? Pretty sure it will be more efficient that way.
Prius has very short on-time for its ICE in urban driving, something like 20-30%, despite the ICE contributing to 90% of the total energy generated (regen is less than 10%). In the city it almost operates like a EREV; the engine turns on in brief bursts to generate electricity for the battery. The energy taken away from the electric SC during this period is negligible compared to the energy consumed by the motor.
Of course, on highways it's more complicated, since the engine acts as a prime mover AND a sustainer for the motor. In this case an electric SC is less efficient than a belt driven one (due to more pathways for losses). But there will always be some compromise involved in hybrid system design. There is no solution that works best in all scenarios. It will be great if they can do lean burn with natural aspiration, but alas they cannot.
I'm more inclined to them using a belt driven supercharger like Mazda does just because it's proven technology. The point is, a belt driven supercharger always needs to take power away from the ICE, but electric SC can take energy from regen or the plug.
The supercharger doesn't need a 300HP motor like the drive system. I would expect an electric supercharger to be a drain more comparable to an HVAC blower. Regen braking would easily keep it topped off in city driving, as
@ssun30 said.
Actually, boosted lean burn requires quite powerful compressors. The paper didn't specify how much power the SC consumes. But if you just look at the air oversupply ratio, it's close to supercar turbo level. For a 30:1 AFR a 2.0L engine is sucking in as much air as a 4.4L. But this only applies to low-load scenarios, when load is high the SC disengages to produce a stoichiometric mixture (they want to avoid the 15-30:1 region where NOx emission shoots up). I think this is also why a turbo is simply unfeasible, as at low-load there simply isn't enough exhaust energy to spool up the turbine. The engine will have horrible response.