Depends on the car – I’m almost certain later model Priuses have an electric compressor for A/C. Eventually the battery will get low enough and the ICE will start to charge.
Also worth mentioning that in the Prius (and similar systems) the ICE doesn’t just come off when stopping, it could also not run when going down a hill. Motive power is constantly switching between electric, ICE, or both, and the ICE can be moving the vehicle and/or charging the battery.
The ICE is (I think) sped up considerably more than most ICE starters before ignition.
The only time I notice is when I’m trying to squeeze into traffic and I need to move fast. The slight delay has almost caused me to crash. The same move when I turn the ASS off is no problem.