Hello.
The answer is yes, you can use a 12V power supply of any amount of Amps that is greater than or equal to the amps of the LED lights. So if a LED strip uses 2A (two amps), you will need a power supply of 2 amps or more. A 4A power supply can even drive two LED strips. It will work correctly, but there is one thing to verify:
If you use a battery charger this may not work correctly. A 12V charger might not start if only connected to a LED strip if it is automatic. Verify if your charger is indeed a Battery Charger and not a power supply. If it is a charger, I do not recommend using it.
If it is a "power supply" and not a "battery charger", then this will work immediately.
Also, you cannot use a potentiometer for such a high power application. Potentiometers for a setup like this will need to be huge, and are usually non-existent. Use a qualified PWM dimmer for your led strip. Also, check if your strip is actually dimmable. If it is not dimmable, dimming it might cause your leds to fail prematurely.