Yes you should be able to connet the Outputs from your module into the Ins on your mixer just like any other instrument. I have not used Reaper but assume you just set up the soundcard connections and select the audio channel with the module on it - at least that's how I would do it in Cubase.

Just do a couple of test records to make sure audio is coming though on the correct channel before getting too involved (I have done this before and wasted a whole session by not having the correct line selected).