FM transmitter question?

I Just bought an fm transmitter and since i hate the stupid plug and
all the wires i hard wired it to the car. first is this safe? also my
power supply to the transmitter is always on even when the key is out.
and the red LED on the transmitter is always on. My main question is,
is it ok to leave it on all the time?, and will it drain my battery? i
already did it to my sirius radio. My transmitter is a Monster brand
one, i provided a link below for reference:

http://www.radioshack.com/product/index.jsp?parentPage=search&cp=&productId=2110504&origkw=fm+transmitter&kw=fm+transmitter&tab=summary

Thanks!

.

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