If it's over filled then I guess it's possible the pump could push it up out of the overflow I think there's a overflow blow off assembly in the cap. You want to be sure it's filled to the full line and not way up to the top.
As long as it's on the underside of the cap inside of the reservoir with the cap screwed down you're probably fine A little air gets to that stuff and it can get a little crusty Rinse it out if it makes you nervous and put the cap back on Make sure it's tight. You want minimal air in the system.
I wonder if that might happen if the loop wasn't bled properly. Bubbles that get into the tank will rise to the top, burst, and could send a little coolant up onto the cap. Driving on a bumpy road might do that too.
There's no bleeding per se when you change the pump pour the fluid in a little bit above the full mark turn on the car the pump will automatically suck the fluid in it pump it around the circle you'll see it go back into the jug you'll see the jug settle and that's where it will stay while it's running if it's not on the full mark put it right just till it touches the floor mark close the cap if you want to you can leave it running for another 30 to 60 seconds to watch it then turn the vehicle off and you should be done for a long long time there should really be no bleeding The pump is a mag drive type of pump so you're not damaging the impeller for the few seconds that it's running dry pulling the fluid into the pump and pushing it out the other side and back into the reservoir really.
I bled mine. Run a bit of tubing from a valve at part of the loop into the open container next to the inverter. It takes a couple of minutes before all the bubbles are gone. Not that there was a lot of air in the system when I changed mine. I would expect much more air if the whole loop was drained and refilled.
I mean you're dealing with 3/4 or 5/8 ID hoses here for the most part so this air that's in between one hose and the pump and the output hose that should only be there for a couple of seconds literally and there should be no cap on the reservoir there's no possibility of overheating and water flying up and hitting you in the face or anything because well it's just not that kind of system so the air that's going to come whooshing through You pour in the coolant should come right on through the hose through the inverter with coolant coming behind it because you're pouring it out of a jug and then it comes right back into that said jug the air that is so I think a lot of people don't pour the coolant in the jug very smartly they try to add a little trickle or something or they're dumping it too quickly and overfilling the jug and waiting for it to settle glug glug glug If you just add it right smartly it should feel right up through the inverter and up to the full mark on the reservoir in seconds and then if you want to be safe you squeeze the hose right at the pump both of them if you like and then if you see the level drop a little bit and hear a gurgling noise put it back on full. Now just turn on the car and there should be no bleeding if you will at least that's her experience here.
I think there must be something a little funky about the inverter coolant loop which led Toyota to put the bleed valve where they did. If it acted like Tombuk2 says there would be no reason for that bleed valve to exist, the system could be bled just like a normal car's engine coolant loop (as he described).
