Does the inverter coolant pump run whenever the car is in Ready?

Hi all, apologies in advance for what is probably a dumb question, but I've been searching/reading for close to an hour and still no definitive answer...

In short: I swapped the original 12v battery on my 2010 Prius today after a few intermittent instances of getting a red power button light and failure to start on cold mornings. Since I had the hood open, I checked the coolant reservoir flow, and found none. The level wasn't even approaching the "notch", and if I understand correctly there should be a small "waterfall" from back to front?

So: is it correct that the coolant should always flow when in "ready"? Most references say I should test in Ignition-on mode, which for reasons that I won't go into right now (long story), isn't an option for me.

Am I going off track somewhere here?

Thanks!

 

Thanks!

 

Thanks for the additional replies. I actually went so far as to setup my iphone and took a video while I cycled the car on/off.

In the video I can see that the right(US driver's)-side "compartment" of the coolant tank rises noticeably and the left side drops while the car is switched on. I take this to mean that there's coolant flowing, although I would have sworn that when I looked at this previously there was a definite "waterfall" through the little notch visible through the filler hole. Maybe I just need to add a bit of coolant to raise the level up enough to reach the notch...

Further confirmation was had by snaking my hand down in front of the inverter and touching the pump, which could clearly be felt to be "doing something".