Can head gasket replacement cause water pump to fail?

I have a 2012 Prius Four with 170k miles. It's been great, no major repairs until now.

A few months ago my coolant level started slowly draining, so I would add some coolant every couple of weeks to keep it full. Eventually my high coolant temp light came on briefly a couple of times, so I took it to an independent shop, they did a test and said the head gasket is leaking. Then I took it to our local dealership without telling them I had already gone to another shop - they also did a test and said the head gasket was leaking.

Since the cost estimates were about the same, I decided to spend $5k and have the dealership replace the head gasket, which took 2 weeks. Then I was really hoping I wouldn't have to do any unscheduled maintenance for a while and could just drive the car for a few more years.

After getting the car back, I made a couple of very short trips and everything was fine. Then I drove about 40 miles. Driving there I had no problems. On the way back, the high coolant temp light came on a couple of times for 10-20 seconds each time.

When I got home I looked under the hood and the engine coolant level in the reservoir was near the bottom of the tank, which is far below the "low" line. So either the dealership didn't top off the coolant when they did the repair, or I had a serious leak.

I took it back to the dealership and they said there's a code indicating that the coolant pump isn't working, so it needs to be replaced. He said when I brought the car in originally they checked everything and there was no code for a water pump problem. Their normal price for a coolant pump replacement is $1200, but they'll do it for me for $900.

To me, it seems like a very hard-to-believe coincidence that the water pump failed immediately after the head gasket was replaced - just based on timing, it seems very unlikely that this was a random failure. Is it possible that the dealer did something during the head gasket replacement that damaged the water pump? I know there's no way to prove that, but I really don't like the timing of it. If I only had the dealer's diagnosis of the original problem I would even suspect that the original problem was a failed water pump and not the head gasket, but since another shop also independently diagnosed the problem as a head gasket leak, I have to think that there really was a leak. But this water pump failure on my very first long drive after the head gasket replacement seems like such a crazy coincidence. Also, would a water pump failure cause a lot of coolant to leak out? Because I still don't know if the dealer didn't top off the coolant when they did the repair, or if it leaked out very rapidly somehow.

Any opinions or relevant experience would be greatly appreciated!