I'll chime in.... Chris, sounds like your asking if it's ok if your aftermarket headunit displays the date/time even while the car is off.
I'm going to say that it sounds like you didn't hook it up correctly. I can only speculate about the drain on the battery. Or about your iPod charging.
I would read some of the other installation posts and figure out what you did wrong. As I know that the 12v DC connections are powered off when you turn off the car and your headunit should be off also.
Let us know what you find out.