I think it is definitely technically possible - if you have written software for the necessary format conversions. I haven't looked into it, but I doubt that the PC version and Sega CD version use the same data formats for levels. They certainly don't for music and video. Well, the music is CD audio, but all the "past" tracks in the Sega CD version are actually special BIN files that are similar to MOD files, if you know what that is (basically some digital audio samples plus note data with playback instructions for those samples).
I fixed the old PC version of Sonic CD once before, to make it playable on Windows XP. But it broke again and doesn't run on Windows 7 or 8. However, a while ago I applied the methods I originally developed for Ecco PC to the PC versions of Sonic CD, Sonic 3D Blast, and Sonic & Knuckles Collection. Meaning I got those old games running perfectly fine on Windows 8.1, with a few minor improvements even. So, instead of porting stuff from Sonic CD '96 to the Sega CD version, you can just keep playing Sonic CD '96 on PC. Once I release my patch, at least.