best thing to do would be to check with the dealership,
but I think a good way to protect yourself if you decide to go with it, is to buy a capacitor. Have about 1-farad per 500W RMS. Not only will it protect you from taking huge draws at once from your hybrid battery, it will make you system sound better by never wanting for juice during a major bass tone. This in most cars would be seen as the headlights dimming.
Since we don't really have an altenator (i think), we use the IMA motor for all our electical needs, and that little battery up there in the engine compartment is purely for the backup starter in the event your IMA battery is depleted or there is a malfunction in the IMA system and it has shut itself down until you see the service department. So the capacitor would be very good for protecting this tiny power source (normal battery).
You could never have too big of a capacitor, but you don't need to go crazy unless you just have that kind of money. A 1.2 farad runs $100 up to a 40-farad at $500. So that would give you stored energy for a 600W system to a 20,000W system.
I really don't see why you couldn't (have a system, and others do), especially if you have it professionally installed. Your system would sound best if you replace the door and rear speakers and ran an amp on those as well. I don't think there would be any advantage of running the head unit through the capacitor power supply, but I don't think it would hurt. If you want to go really crazy, you could get components for the front (and rear if you like) and mount the tweeters somewhere higher up for better soundstaging and Sony also makes head units that you can enter in the distance from the speaker to your ear and it adjusts when the speaker recieves the signal so that all the waves for that note hit you ears at the exact same time.
Here is a link to the Crutchfield capacitor page
http://www.crutchfield.com/S-DhQCewR...sp?g=725&avf=Y
Even if you don't want to buy from them, they have great resources for learning about products and technology. If you do order from them, they give you free connections most of the time, free lifetime support, free phone support. I can still get info and support on an amp I bought from them 6 years ago.
I am getting tired, so I apologize for the length

I can go on and on when sleepy
