It entirely depends on the captain and whether he thinks the ship is still sailable.
If the damage is slight or if only 1-2 compartment is flooded, the ship may be able to continue at close to full speed. In WW2, you had many accounts of major warships (CVs or BBs) being hit by one torpedo and continuing on with little loss of speed.
On a smaller ship, say a cruiser or below or a merchant, it may be more of an issue. The torps will normally hit on one side and cause flooding on that side. If a ship continues on at full speed, there is the risk that the sea pressure may cause bulkheads to collapse increasing the flooding or that it may capsize.
This is even more of a problem with merchant ships which usually don't have the same watertightness as a warship and which has a civilian crew which has not been trained to handle such emergencies.
The normal course of action would be to slow down or stop the ship to assess the damage, perhaps counterflood compartments on the undamaged side to prevent capsizing and resuming course, if possible.
The problem in a game point of view, is how to program the AI to act like a real captain.
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