Can I get my car's head-unit to play audio, via USB, from my Galaxy S3?
Yes and no. The fact that your Galaxy S3 does not support mass storage mode means that you cannot play audio files stored on the S3 with the radio, like you could with a USB stick. (If your car's radio supports mass storage, that is.) 

However, the other type of USB connection, allowing your iPhone to be controlled by your car's radio is an Apple Accessory connection. This is a protocol for communication between Apple devices such as the iPod and iPhone and accessories like your car's radio. Android currently does not support the Apple Accessory connection, but has it's own protocol for communication with USB accessories. It might be technically possible to create a solution for Android to allow it to speak with Apple Accessories, but currently (as far as I'm aware) no such solution exists.