Hi Blake,
Yes, it is possible to extend the microphone. You can use any interface on the floor box like XLR connector or just like in our case we used DB-9 along with CAT-6 cable on the floor going to the codec mic audio interface and it works perfectly.. As long as pin-outs are terminated properly and it should work. The reason why we decided to use DB-9 because the connector is more lighter rather than XLR.
And yes, it will work also with DSP's like BIAMP or Clearone. But the only thing it will not work is the muting button for mute/unmute functionality because DSP will not provide power or connection for that but the audio will work.
regards,
Acevirgil