The VideoLAN Forums

Is it possible to add a Codec into VLC's transcoding list? If so, how?

You need to add a new encoder or codec module to VLC's source code, thus it is impossible to add new encoders to existing binaries of VLC.
Additionally, you need to add an entry to your encoder in the respective GUI of course.

BTW. Such a module would need to be covered by a GPL-compatible licence in case that you wish to distribute the modified source or binary version.