Certainly that can work. When you do it that way, there is a potential bonus feature. There is likely an option in the FAX software you can set for this. You can choose, when a FAX is received, to have it stored on your HDD in a particular graphical file format (often a .tif) and NOT printed. Then later you can examine each of those files on your screen, delete any junk, and print out only the ones you need. That way your printer does not need to be on all the time.
You MAY need one more component. For generating FAXes to send, most software can be used. Windows itself has a FAX "printer" device (actually a software driver) you can use to "print" your FAX from an application. When you choose this printer, it does not print. It gets the...