Usually this does work but you should know it's not 100% foolproof and in rare circumstance could burn up your power supplies regulator. The typical battery charger is not regulated. This means when you put a dead battery on the charger, it will want to draw full current from the charger. Because there is no regulation, the voltage will fall back a little and so does the current. As the battery begins to develop a charge, it draws less current as the voltage rises.
The regulated power supply will struggle to maintain the full 13.8 volts while charging a dead battery. Its voltage will not be able to drop and provide a lower current at the beginning of the charge cycle. That could cause the pass transistors to short, triggering the crowbar over voltage that will then slam a short right on your battery too.
If you proceed with doing this, my advice is to monitor the power supplies temperature when charging the battery from a discharged state. If you can keep your hand on it, you're probably OK. All of this is dependant on the particular power supply being used. Many do have current limiting that would increase the chance of success. Some may just shut down when the current is too high. Others with no protection could just blow up.
