Well it really would depend upon a lot of factors.
Where is the damage is an how much damage there is and how hard the pilot is pushing it.
If it's at the bottom of the cooling system all the coolant would drain out and the engine would die really quickly. If it was at the top of the system it would take a lot longer for the fluid to drain and the engine would go on for a lot longer.
Even though the Spitfire IIA had a pressurised cooling system if punctured it would still work like the unpressurised system in the Mk I as long as the fluid was still circulating.
There is a story about a Australian P-40 pilot in North Africa that was shot at during a straffing attack and his motor over heated so he landed. Seeing this a German motorised patrol went to pick him up. Before they got within range, the Australian took off and flew for a little while before the had to land again, By the time the persuing Germans got to his new position, the engine had cooled down enough to risk another short hop. Eventually he got over the front line and the Germans gave up and retreated. (The pilots name was John Waddy of 112 Sqrn)
So I guess the answer is "It depends"
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