Applies to: ReMOTE
No, they do not.
When the ReMOTE is used in controller mode it can send MIDI data but will not respond to it. MIDI data sent back to the ReMOTE from your DAW/sequencer can only be routed to the MIDI out ports on the back of the ReMOTE.
The ReMOTE only communicates with your software in a one-way fashion when in controller mode. This means that if you use a control on the ReMOTE to control a software parameter and then use the mouse to alter that same parameter, the value of the control on the ReMOTE will not update after changing it with the mouse.
The control will remain on the value it was at after it was last operated by hand.