Air Conditioning system

no problem at all. BLAST the AC full on MAX and ENJOY. As long as your refrigerant level is 100% full.

 

Toyota did a great job engineering the overall cooling system such that you can run the A/C in all driving circumstances as long as the cooling system is kept in top condition.

Once you've got ~10 years worth of mineral scale clogging the radiator and a little bit of refrigerant has bled out of the A/C system?

Then those signs along I-15 become useful advice once again.

 

Yes.
And that "old tale" goes way back to the 1950's and hasn't really been a problem for about 50 years or so.
Except maybe with a REALLY old vehicle who's cooling system is way down from it's original capacity.

 

Seems like there are two overlapping questions about shutting off A/C for "load". One involves shedding the A/C load for a brief stretch when you want maximum available power for passing or the like. That's a pretty old trick and I've had even older vehicles with belt-driven A/C that were wired to automatically interrupt the A/C at moments of full throttle. I'd be surprised if the computers in a Prius don't have some similar logic too (and with the variable-speed compressor in the Prius, they aren't even limited to just on or off, they could also just partially back off the A/C power). When those features are built into the car, that pretty much excuses the driver from thinking about it at all.

The other question concerns a long stretch of high-power, hot operation, and whether engine cooling stays adequate. The A/C condenser is ahead of the radiators for the engine and electronics, and if the condenser is shedding a lot of heat, that will reduce the radiators' cooling ability some. As a practical matter, I don't think I would worry about it unless I had ever seen the overtemp light come on. I don't think it's likely unless in pretty extreme situations.

If I were in extreme conditions and did see the light come on, then yes, I would consider all reasonable accommodations to improve cooling, and dialing back A/C or turning it completely off would be among those options. (So is cranking up the cabin heat, though it doesn't make the humans happy; it works, and I've used it when necessary.)

About "does not run on engine power", even in a Prius (as long as it isn't a Prime, or the earlier Plug-In), there isn't any energy used for anything that didn't come from the gasoline engine originally. Compared to a conventional car, the Prius has more tricks up its sleeve to buffer up some of that energy, use it later, and plan when to replace it, but it still came from the same place. (I'm not counting the small amount of energy the solar-panel-equipped Prii can use to run ventilation when parked. That doesn't come from the engine, of course,)