I will NOT be bleeding the system after changing inverter pump...IS THIS A PROBLEM!?!?

i think you'll be fine.

 

It's not clear what you swapped - your title says the inverter pump, your actual post says the inverter. Which got swapped?

The only reason you don't want air bubbles in the coolant circuit is the same reason you don't want air bubbles in your veins ... they can end up circulating to a location where they stay (for example, a local high spot) and impair the necessary flow to nearby locations. It wouldn't be likely to cause any kind of problem other than possibly inverter failure, and maybe if your cousin finds it easy and relaxing to replace inverters, that won't be a problem.

You can bleed it yourself pretty easily. There are two bleed valves on the front of the inverter. There are posts here about how to do it. One of the bleed valves is pressurized (any time the pump is on) so the bleeding from that valve is easy. The other valve is on the suction side of the pump and has to be treated a little more cleverly; if you just open that one while the pump's on, air will go in. Again, there are PriusChat posts on the procedure.

-Chap