It's possible although your plugpack maybe a regulated 12 volts while a charged battery will be 13 plus a little volts .
suggest measure the current drawn at 12 volt and again on the battery. be quick as if the current is higher, you may damage the led.
calculate the power in each case, volts times amps.
if they are similar, all is good. if they are different by much, you will need to provide either a current limiting resistor or some kind of regulator.