Q: Timing cover and coolant leak questions

4 months ago I had a hose leak and got it fixed at a Nissan dealership then some months go by and I had my oil changed and the mechanic commented on smelling coolant at the same Nissan dealership but no one bothered to check any further, then a few more months go by and my check engine light comes on and I bring it back to the same dealership and they said my timing cover is bad needs to be replaced and it will be about $4,000 but they said it wasn't so bad that I couldn't drive it for a while and they cleared the code, so I brought it into a different Nissan dealership and at that dealership I find out that the hose that the original dealership fixed back in early summer never was clamped so coolant had been slowly leaking wherever in my car and I never noticed it on the ground so I'm guessing it must have been leaking into the engine or something. So my question is could the coolant leak have caused my timing cover to go bad?

My car has 119000 miles.
My car has an automatic transmission.