Sure its possible. Its called Online Faxing. All you need to do is have the user scan a document to themselves just like they normally do (assuming they start with a physical document). When they are ready to fax you have them forward the attachment via thier email client with a special email address. The online fax vendor will then handle the physical fax sending and recieving for you. Everything gets managed from the email account of the user. You can online fax directly from the control panel if you route things correctly on the network.
More info with Online Faxing:
Now if you want to make it complicated and try to setup the fax card on the printer to talk to a faxing client on the users machine that is something else. The faxing client (of which there are many) needs to be installed on the users machine. The fax client must also be able to find the printer on the network. You wont be able to manage this kind of a connection through your print server. HP has a product called DSS that manages the scan and fax profiles on a printer but those options are only available on teh control panel of the printer, not the users machine itself. After you install and configure a fax client on the users machine you can use the normal TWAIN scanning features to send fax jobs to the fax modem of the printer.