Probably not with this device because it does not support ARC.

Is this a surround system? Where is the source(s) physically located with respect to the projector? 

>> Probably not with this device because it does not support ARC.

So wireless hdmi devices are spec’d to some lower standard of audio that allows for audio passthrough on simpler devices but not the Sonos Arc because it uses a stricter audio protocol?

>>Is this a surround system? Where is the source(s) physically located with respect to the projector? 

The speaker set-up is a surround system (Arc + Sub + One’s).

The projector is a smart projector and is its own source of video and audio.

Because of the cable issue, I currently have the projector located on the same side of the room as the speakers. Projector connects to Arc via cable, everything else is wireless.

ARC (Audio Return Channel) is a two-way scheme that allows the TV or projector to send audio back to the receiver. Normally, a receiver would send audio and video to a TV or projector, however, modern TV’s now include Apps that need to be able to send audio back to the receiver. Both the receiver and TV or projector need a special chipset to support this. Older units do not include these chips — that did not yet exist when the unit was manufactured.

This complicates your application because the wireless HDMI links are only one way. I’m not aware of any wireless HDMI-ARC or HDMI-eARC links.

Thank you for the reply. Still trying to wrap my head around this.
From my perspective, I only need one way flow (sending from the projector → Sonos) - are you saying that the Sonos needs to send audio back to the projector?

No, the TV has to send audio to the Sonos via HDMI-ARC, which is a whole different channel than what sends audio to the TV.  For example, if you connected a streamer or Blu-Ray directly to the Sonos, you get no sound whatsoever.