I don't think it's the case, but I've become paranoid that shutting the engine off without first shutting off the radio drains the battery a bit, becoming a factor in very cold weather. I had to buy a new battery the other day, that's why I'm checking.
umm, no. the radio has two circuits- memory and power. One circuit is only live when the key is on and one is live at all times. The factory radio uses a low amp wire for memory and switches a higher power circuit with the key for the other functions, but many of the newer radios have a high amp circuit that is live at all times and only draws real power when the key is on (there is a switched circuit inside the radio that powers the other functions with the key.) If you think you have a parasitic drain, you need to check it with an ammeter.