It would be possible on a Duet 0.6 because that's what I used to prototype the WiFi support initially. But it would need a special firmware build. It might be possible on RADDS but there would be other complications, e.g. no high speed interface to the SD card, and having to find a way to share the SPI bus between the esp8266 and the SD card.
It's possible to connect an esp8266 to the serial interface of the RADDS or Duet and run most of the web interface but with limited file upload and download capability. See the thread by toxuin in the Developers section of these forums for details.
Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod
Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].
