Fax only call queue?

I’m trying to set up a call queue that is exclusively used for Faxing.  The members of the queue should never have this queue ring their phone, and it should never accept a voicemail.  Just send and receive faxes.

Is this possible?  I think I have some settings to do this, but not clear if this will work.  Honestly, I’m surprised this isn’t an option out of the box.  

TIA for any help/helpful suggestions