Can a bad water pump cause code P0117?

Hi there. I am trying to sort out a problem that struck a couple of days ago. I had just gotten on the highway when the red triangle of heart pounding fear came on, followed by the overheating light. I got off the road at the next exit which was almost immediately available. Sitting at the light about 30 seconds later, the warning lights turned off. I slowly made my way to an auto parts store but there was no code to be read. I drove with very frequent stops to my destination with the same things happening. Using the engine to go up a hill earned me the lights and getting to about 40-45 mph did too. Stop for a minute, no lights. Also it’s worth saying that there was no clear overheating smell either. So near the destination the Che k engine light finally came on and I went directly to have the code read. P0117. I was excited it was probably just a sensor even if it’s going to be a terrible pain to get to. However I noticed the next morning that my serpentine belt was gone and discovered it mangled at the bottom of the engine housing. Too, it looked to me like there was very very little coolant. The overflow container was nearly empty and I didn’t see any by looking in the radiator. Anyway, ignoring that last bit other than adding more coolant, I was excited again because the serpentine belt is easy to fix and I figured that was probably causing all of the issues - not the sensor. I replaced it, filled the coolant and headed back from the original destination only to have the lights come on again. I made frequent stops, took back roads and did all I could to make sure the battery power in the car was used more than the engine. When I got home I saw that the serpentine belt was loose then noticed that it’s already been torn. I also noticed that the water pump pulley is absolutely not in line with the other two that the belt connects with. (Tensioner and the crankshaft pulleys) It appears that the top of the pump pulley is sort of leaning out and the bottom is closer to the engine than I think it normally is.

So I’m wondering if the water pump may have gone so bad, in fact, that it’s possibly crumpled in on itself. I know it could cause the loss of coolant (which I think I spotted at the bottom, though not on any pavement where I’ve parked) and of course the overheating symbol. The misalignment would be the culprit for eating the belts. I am planning to buy another water pump but if this brings some other issue to mind that I should consider I’m all ears! The only thing leading up to now that’s been noticeable is that the car has been using the engine much much more than it needs to. It’s always a relief when it shifts to the battery. That’s been going on for about a year or so.

In this image you can sort of see the alignment issue of the water pump pulley behind the tensioner pulley.