If you have a number specifically for fax, call it 111-111-1111, you could forward that number to the free CallCentric number. Let's say that CallCentric number is 999-999-9999.
You would then set up a call treatment to say:
If the calling number is 111-111-1111 then it's a fax.
Otherwise the call is coming from a person and send the call to an extension, etc.
In this case, you would lose the caller id of the person who dialed 111-111-1111 and just see 111-111-1111 as the caller ID.
I am doing something similar as this. I have an 808 area code number call it 808-555-1212 with
Voip.Ms that I want to use for Fax, but
Voip.Ms does not handle fax. Rather than forward the call to CC and pay a couple pennies for a transferred call, I send the call via a URI directly to my CC number. A URI is similar to a URL but in the format
17771234567@in.callcentric.com (this example uses the CC account number). Then at CC I just say if the call came in from the 808-555-1212 number, it's a fax. If someone calls the CC number directly, it is a voice call (which may or may not also get some kind of call ID treatment).