You need to keep an eye on your gauges. Sometimes the effect is not instant, but there is an effect...
If your radiator get's hit, your coolant runs out in about 1 or 2 minutes. After that your engine quickly heats up. Once it hits 150C, it seizes.
If your oil get's hit, your oil press begins to drop. It varies by aircraft how long it takes to empty. Once your oil pressure reaches 0, your engine will stop.
If your fuel tank(s) get hit, the fuel will begin draining out. You can cycle through your fuel tanks (Shift F) to see the hit tank draining rapidly. Once all your fuel is gone, your engine will stop.
There is no hydraulic system modeled, which is too bad.
There is no oxygen system modeled, which is also too bad.