Depends how you wire up the LED.
If in series, no current addition, but you do lose voltage. If you put a red LED in series, for example, and are sinking current, then you will end up presenting a low of ~2V to the card. Will that generate enough current thru the relay's optoisolator or whatever it uses to turn on?
Insuffucient data is available on the relay card to say if that would be an inpact.
On the other hand, adding a high brightness (the 5000+ mcd variety) LED in parallel, they would need only a few mA to turn on & provide indication of being on.