Sonso ACE and Sonos Radio HD?

Not directly, no.

You could buy a Port and 3rd party bluetooth transmitter along with the Ace.  The Port plays Sonos Radio, transmitter sends the audio to Ace.

Or, you you connect a Port as input to a TV, with Arc connected and Ace bonded to that.  Sonos Radio playing on Port would technically be “TV audio” to the Arc and thus it can send it to Ace.

Perhaps my favorite would be to get an Amp + speaker wire to RCA adapter + RCA to bluetooth transmitter + Ace.

Oh, wow - thank you. 

It kind of baffles me that their headphones are not really compatible with their services. 

It’s beyond bizarre that the ACE does not support audio over wifi. I can only assume there were technical difficulties they couldn’t solve. I know my SONOS Roam is constantly dropping from my network and I’m forever restarting it. But for the ACE it’s so disappointing. I love SONOS Radio HD but have always wanted to be able to listen via headphones. I also listen to my CD library through SONOS via a NAS and had assumed the ACE would allow me to finally do that on headphones. But it is not to be. Perhaps down the road. 
 

A Port and a Bluetooth transmitter and an ACE is a very expensive workaround. 

Yes you can play Sonos Radio to the Sonos Ace.
Your Sonos Ace is connected with Bluetooth to a device. Say an iPad. 
Open the Sonos App on that iPad and start Sonos radio. 
The audio outputs to Sonos Ace.

I have the Sonos Roam connected with Bluetooth and it appears on the Sonos app. It shows that it’s playing Sonos Radio over bluetooth. 

Following the disaster of the new app, and the utter contempt for how the customers have been treated by Sonos, the chances of me buying the headphones were slim at best. 
However, being unable to listen my my NAS music library on them is bizarre to say the least and chances of purchase are now zero. 
 

Really poor thinking by Sonos.