The volume is a hardware function. When you turn it to maximum using the volume controls it's at maximum power that the circuit in the phone can produce. You can run apps that claim to increase the volume, but all they really do is increase the drive to the amplifier, increasing distortion - and your brain interprets that as an increase in something. Since the app claims to increase volume, you accept that the something is volume - it's not.
It's like increasing the power of your car engine because you put purer air in the tires, or something. Rooting won't change the gain or output power of the audio amplifier, it'll just let you run apps that need root. (All it does, in essence, is add a file to Linux [which is the operating system that the phone is running] that Google chose to leave out - su. It doesn't change any hardware values - like resistors - which is how you increase the audio output.)
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