The head unit does not need to have a direct connection to the battery. If the radio was conected directly to the battery, it would have a constant 12 volt source, that's great if you never intend on turning the stereo off. (Party on!) You would then need a switch other than the ignition switch, directly wired or signaling a relay. The constant 12 volt (yellow wire) memory retention (clock and presets) has such a minute draw, direct to the battery for this is futile. Even if your head unit says "1000" watts X 4 (total bullshit) the factory supplied switched 12 volt wire is more than ample.
Using a outboard amplifier is a absolute different story.