Some comments from the standpoint of an ignorant person watching smart people work on this:
  • It can be done.
  • You need to start with WinRE rather than WinPE. (No, I don't know what I just said.)
  • Microsoft recently removed wireless support from WinRE but it can be added back.
    (Microsoft reasonably does not want to make a recovery system so flexible that there is no reason to buy Windows.)

I have no specific information, but members of the Acronis user community have developed a "builder" that creates a WinRE system with wireless support (and the Acronis True Image backup and restore software). And I know it works because I've used it. I have no idea how willing they are to share their knowledge but you could ask.