It would be helpful to know what your configuration is and what cooler you're asking about.
Some of our machines pass freshwater through the interstage coolers and jacket using a small circulation pump - then pass the freshwater through a cooler that's fed with seawater from the ship's firemain.
Leaks of air into the freshwater system tend to make the header tank overflow and overheat the cylinders (which causes a loss in delivery pressure on a good day, discharge overtemp trips on the sort of bad day when you're lucky and complete collapse of outlet pressure accompanied by rapid unscheduled disassembly if you're unlucky and the cooling is somehow accidentally restored suddenly).
If you've got a FW/SW cooler and that leaks, the most likely effect is ingress of seawater into the FW system. Big leaks will be detectable quickly as the header tank overflows. Small leaks are more insidious, and your headache is going to be internal corrosion (which will eventually make the machine run hotter, but will take it's time to get there).
OP. Would you run your car without radiator cooling?
It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)
Actually, it is not necessarily a problem to remove the jacket cooling in the short term. The vast majority of the heat generated in a reciprocating compressor is generated by the heat of compression. The heat is carried away by the flow of gas. The heat is removed in the inner and after coolers. The jacket cooling is tiny in comparison. It is most necessary for start-up to ensure that the cylinders are hot enough (well above dew point) to avoid liquid condensation in the cylinders. We have five large reciprocating compressors that share a common circulating cooling system. Each compressor is about 2000 HP. We have operated for several hours without the jacket cooling system with no negative affects. It is most important that the compressors are fully loaded so that the gas flow will carry away the heat.
