When the PLC output is off, the output terminal is pulled up to 24V via a 10K resistor. If you connect the output to the LED then the LED is presented with a reverse voltage of 24-12 = 12V. Although this will not turn on the LED, but most LED are specified with a maximum allowable reverse voltage of about 5V. While I don't think a weak pull up voltage will cause any damage to the LED we won't know the long term effect.
So if you want to connect the LED to 12V power supply, you should connect a rectifier diode in series with the LED. The rectifier diode can tolerate much higher reverse voltage and will protect the LED from the 12V reverse bias when the output is turned OFF. When the output turns on, the current can flow from the 12V power supply through the LED and the rectifier into the 0V of the PLC power supply. Note that the LED 12V power and the PLC's 24V power must have common 0V.
LED 1N4001
+12V ----|>|--------|>|----------- PLC output.
The diode method can also be used when you intend to connect to a load with a lower power supply voltage than the PLC.
