Is it required? No.
You can put labels on the disc, then put it in the printer. But as Hawseman said, why go through all the headache and time required?
For years, I used regular stick on labels and my HP photo printer. The labels came out great for being paper labels stuck on. But they didn't look "professional". The quality of the print was good, but you could tell it was a paper, stick-on label.
When you get good printable media, the Epson R200 (which I use) will produce quality that is almost indistinguishable from OEM. The discs do NOT smear, even when I've run water over them (coastered discs that I use for test prints)
I use Ritek (RG05) 8x inkjet hub printable media which can be found for about $33 per 100 from SuperMediaStore. I create the labels in photoshop, then print them using Epson's supplied "Epson Print CD" software. If you use the Riteks (or pretty much any hub printable disc), the settings in Epson's software is:
Inner Diameter: 22 mm
Outer Diameter: 119 mm
I've done over 100 discs so far and not one has been questionable quality or had any overspray. I even get the refill ink from SuperMediaStore for like $5/tank, versus retail of like $14! Anyways, the hassle and time saved over not having to dick around with paper stick on labels is sooooo worth the couple extra pennies I spend. The printable discs have better overall quality, dry faster, are more resistent to humidity/water/whatever so they don't smear, are always perfectly centered, and never bubble. Another benefit is that the printable surface acts as a reinforcing layer to the reflective layer, as opposed to a paper label sometimes bubbling (as it gets old) and pulling the reflective layer off the disc.
Just be sure you get INKJET hub printable and not THERMAL. I made that mistake once. Whoops! The printer don't like them discs!!!