Yes it is possible but not perhaps in the way you think. It could be the DVM or the circuit driving the LED side of the relay, the likely cause is more than 5V being put across the LED in the reverse (non conducting) direction. Many DVMs use 9V batteries and a resistance check or 'diode test' on these meters often puts the whole battery voltage across the device under test and sees if it conducts by measuring how much the voltage is dropped to. In the case of an LED, in the forward (conducting) direction the voltage will be dropped to about 1.2V but in the reverse direction it will not pass current and not drop the voltage at all, at least until the until the PN junction is destroyed! the maximum reverse direction voltage is 5V.
I would suggest wiring a normal silicon signal diode such as the 1N4148 or it's equivalent across the LED side of the switch with the diode 'pointing' the opposite way to the switches LED. This will clamp the excess voltage to a safe level if the polarity is accidentally reversed.
Brian.