Yes, you can play as Super Sonic, Super Knuckles, and oddly enough, Super Tails. The only thing that requires this is the use of Level Select, because there is no way to activate this otherwise. In level select, you can either initiate Debug Mode, or change options in the game that Christian Whitehead doesn't allow you to change otherwise. These include:
The option to change player, despite if you didn't unlock Tails or Knuckles.
The option to turn On and Off the Ground/Air Speed Caps, to make it more retro.
The option to turn On and Off the Spike Glitch that was originally in Sonic 1.
The option to change the item sets during the game, which include Sonic 1, Sonic 2, Sonic 1 + Sonic 3, and Sonic 2 + Sonic 3.
The option to change the Max Emeralds from 6 to 7, which isn't available otherwise.
I hope that clarifies some things.