As Holocron said, no it wont be visible unless you tell it to be.
now as for what is better a USB or an Ethernet based printer. Well each has advantages and disadvantages. Biggest is cost, Usually a USB based printer will be substantially cheaper then a Ethernet based printer. Both can be networked (shared) the difference is that the USB needs to be plugged directly into the back (or Front) of the computer to the USB port, the Ethernet printer can be anywhere on your network. Both will need a print server to spool the print job.
In my experience a combo printer/fax/copier Are quite troublesome, if the fax worked it didn't print right, if the copier worked the fax had issues... stuff like that. I have always been a big fan of components rather then one big piece. the convenience factor is lost however in having a separate fax, copier and printer... Just like with a high end stereo system, if you buy the pieces separately, you will be able to get better quality then if you buy one big unit. (not including Bose)
as I see one manufacture may make a good quality fax, but they may not make the best printer for the money....
that is just my opinion though.. If you are tight with space, and really need a fax AND a printer AND a scanner AND a copier, the a combo may be for you...
but don't forget your computer can send AND receive faxes... how much do you really need to copy... can't you go to the nearest 7-11 and pay the $ .10 per copy. I would pool the money and buy a nice higher quality printer thqt can also print phot quality... that is what you are going to use the most anyway.......
sorry to ramble on.... as eveything else in life you must do what works best for you....