Will line conditioner do anything for the other receptacle in a duplex?

The purpose of the module type power conditioner is to clean the AC line from the receptacle to the service panel. That includes both duplexes which are connected.
 Often, multiple modules are used in separate duplexes to reduce noise on other lines which will meet at the panel. This will have an cumulative effect. 

A line power conditioner is plugged into a receptacle, it's function is to reduce noise from the mains to all components which are plugged into this unit. It is only cleaning the AC for your audio system, it does not send a cleaned return signal to the panel.

There are so many different power conditioners, each with it's own unique design.

The EP-250 looks like a good device, although I have no knowledge of its performance.

I’m not sure you fully understand the benefit of this device. There is no preferred conduit, this power conditioner/surge protector "cleans" the noise in all the circuits at the panel. This includes dirty power from outside and noise which has been generated within the house (appliances, furnace). So, noise in all lines is reduced, possibly a modular conditioner is not needed.

The line conditioner plugs into a receptacle and starts its "cleaning" at this point. All components will have less noise and SQ should be improved.

The other receptacle in the duplex is being cleaned by the EP-250 conditioner. The line conditioner serves only the one receptacle, and it is only cleaning the components plugged into it.