A missing freeze plug would cause you to lose significant amounts of coolant. As soon as you added more coolant you would see it dump out to the ground. A freeze plug is pressed into a casting hole on the engine block. The hole opens to the water jacket. (There can be several holes with freeze plugs, depending on engine.) If you lose the plug, you immediately lose all coolant in the engine. You would not be able to drive far before overheating and any attempt to refill coolant would be a waste of time until the plug was repaired. SOME plugs can be reinstalled without removing engine, some are impossible to reach without pulling motor. If you don't trust this mechanic's opinions then take it to another shop for another opinion. Keep in mind, driving it with missing freeze plugs will cause an overheated and potentially ruined motor.
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