Blown head gasket

Every situation is different; even on the same make/model of car, and engine. Some gaskets give up pretty quickly and some may never give up. Others may surrender 6 months or 3 years later; it’s anybody’s guess when overheating is involved. Much depends on not just the severity of the overheating but how long it was overheating.
With an aluminum head or all aluminum engine it often doesn’t take much to pop a head gasket.

My suggestion about a compression test is to make sure you don’t spend $$$$ on this job and then discover the engine has far more serious problems. A blown head gasket will generally affect only 1 or 2 cylinders. This is why you test all cylinders because if the unaffected cylinders show a ring problem (even on 1 cylinder) there is no sense in even considering a head gasket job.