The LED probably draws no more than 15mA, that's 0.015A. By comparison, the interior lights probably total ~30W, maybe less (I don't have my svce man here). But that's closer to 2.3A @ 13V. (P=V*I >> P/V=I >> 30/13=2.30769).
If the numbers are correct, you'd have to leave this modification sitting for 158 days without starting your car to equal that of leaving the interior lights on for 1 day. (somebody check my math on this...)
The point is, if you can leave your interior lights on all night and still be able to start your car in the morning, then this mod should not hurt the battery.