I can't help but think of MUGEN's "Slightly Pissed Off Ryu"- basically, Ryu but his moves have a drunken twist, like falling and landing on the opponent after a Dragon Punch or tumbling over because he screwed up a Hurricane Kick. I guess in Drunk Sonic's case, he could have a fast, hard to steer slide (having failed to roll), or a Thok that has a drunken landing resulting in say, bouncing off floors & walls, or going into that aforementioned slide. It could lead to some goofy shenanigans!
Also, seconded on the Ring Ride idea- I loved those rom hacks!