I am a subscriber of the Artist Plan. Can I register the songs as Content ID?

You cannot register the Content ID of any SOUNDRAW generated music or the songs you make with it. However, do note that you can use and monetize songs from SOUNDRAW without registering Content IDs, so please don’t worry about that!

Side note:

TikTok can act as a medium in which the user can register songs that they intend to use as background music for their content on the platform. 

Since the music uploaded to TikTok must be registered with Content ID, you cannot distribute songs generated with SOUNDRAW on TikTok.

Posting your song on TikTok as a regular post is however totally fine.