Yes you can mail enable the public folder you will be using. As after this the cliesnts having appropiate permission can derive the email from public folder and send too.
More on mail enabled public folder and commands related:
http://technet.microsoft.com/en-us/library/aa997560.aspxManaging permissions:
http://technet.microsoft.com/en-us/library/bb310789(EXCHG.80).aspxYou can configure application running on fax server to forward email to mail enabled public folder and configure its identity as author and yup you should be good.