From what I've read in the manual, I'd say no. Off is off. In fact, if you turn the key to I, you can see the battery light come on, meaning it's not being charged. I'd guess it wouldn't be charged while it was off, too.
It wasn't an academic question. I thought I had seen a case where a dome light was left on and both 12v and IMA batteries were discharged. Must have been wrong.
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