My main question is, is it ok to leave it on all the time?

No.

and will it drain my battery?

Yes. However, the exact design of the model will determine if it is a
problem.

You wired it up to the wrong wire. I assume you mounted it next to the head
unit? If so, there are 3 power feeds you could use.

1. Permanent live (this is what you've used) Often Red.
2. Switched live (this is what you want) Often Yellow.
3. Auxilliary power out (you can use this too) Often Blue/White.

Sometimes red and yellow are swapped (i.e. some Vauxhalls). Sometimes they
are random colours.

The switched live goes with the ignition. The Auxilliary power comes on when
either the stereo is on, or just the radio. It is intended to switch
electric aeriels and amplifiers.

Christian.