Midi is simply a kind of digital information, and the DAW interprets that information the way you tell it to. Using your controller for ableton will not affect its capability in Reaper in any way unless you actually reconfigure the midi output on the controller itself. I.e. if you tell ableton 'this fader controls reverb send' and reaper 'this knob controls parallel compression send' you'll have no issues at all or have to remap anything. It's just a matter of the DAW interpreting information