Yes, inkjet photos do fade, to some extent at least. However, this happens over a very long period, provided that you take some basic precautions in preserving your photo prints, such as keeping your photo prints away from direct sunlight and storing them in UV-protected photo galleries and frames.
If you want to minimize this effect, consider getting a printer with a pigment ink system. Photo prints printed with pigment ink tend to fade less aggressively than those printed using dye-based inks.