Usually damage is noted by poor engine running while it is overheating and the red paint at top of block where head meets block turns brown.

The coolant sensor will melt and usually set a fault code w/check engine light also.

Rapid, total loos of coolant from a busted hose or radiator are the things that kill an engine quickly. Leakage that isn't so total and leaves some water in block usually doesn't do severe damage.

Fill with water and start engine and see if the pressure in coolant system rises almost instantly. This would signal blown head gasket (not a thorough determinant of a bad head gasket, but will tell if it's real bad news).