Air in Coolant System?

[2003S]

If one had an air bubble in their coolant system, how much coolant might one expect to see "burped" out after some spirited runs at a track day?

I had a sub-optimal experience at the track, after getting flagged off for mechanical problems, I realized the coolant was most likely coming from the overflow valve.

I let the car cool, and added a couple of gallons of water, let it sit, and nothing was leaking. Warmed the car up, and went back to the track, and sure enough, after some more spirited driving, it started burping out fluid (now mostly water).

Again, it took a few gallons to fill it up. I think all told I probably put 5 gallons of water in.

Important to note, at no point did the temp gauge read over the "8" on 180. The car did not overheat (mostly because as soon as fluid escaped, I got off the track & cooled it down).

Also, after the 2nd refill, I babied it all the way home, stopping to check level a few times, and it seemed to be fine - a little overflow at one point, but I think I overfilled, so not terribly surprised. Made the 90 mile trip home, without an incident, and took the car in to my guy the next morning.

Other things to know, I had the water pump & a hose replaced a few weeks back, so obviously the coolant was drained / refilled...

Is it possible that air in the system can cause that kind of dumping?