Well… maybe I am missing something. But a dedicated circuit is just that… no additional outlets… that is the point. Now, it is terminated in a duplex receptacle… and you can choose to only use one of the outlets.
I have two dedicated lines… one which has my power conditioner plugged in (with all my non-amp audio equipment), and one for my amp. In the first case I use my mono blocks sometime and use both outlets and sometimes I use my stereo amp and only use one outlet.
But the point of a dedicated line is that, first, there are no other outlets connected to it that might add noise (think about a hair drier), and second the circuit does not wander all over the house acting like an antenna picking up noise.