I don’t think so. I think only WMC is capable of recording or playing WTV files. Pretty sure that MCEBuddy uses the WMC libraries themselves to access the WTV files.
Also, WMC is long dead, unfortunately. Have you considered other media servers? Plex is having a sale on their lifetime pass (good for the DVR features and if you want to view your media over the internet from outside your home network). You could also use Kodi or Emby or something else.
Does PlayOn give you any other option for either downloading the media files directly or can it transcode them to TS or MP4 or some other encoding that MCEBuddy can process?