I don't have that one, but here's what I did install:
http://onemansblog.com/2016/05/16/12...rger-hawk-250/
The LED on it probably draws just a fraction of 1 watt. So it alone won't be responsible for your battery dying. But if you put the battery on a trickle charger it definitely won't matter.
Also, if you buy one of these big ass batteries, it really won't matter...
http://onemansblog.com/2016/04/29/ha...ttery-upgrade/