Soundcloud allows private tracks, ie they are only available by the URL, not in your list of tracks. They still offer an embed code, so shouldn't they embed in xenforo just as with a public soundcloud track?
The answer is really "it depends". Soundcloud uses oEmbed for embedding, so the HTML we receive mostly comes from them. Do you have an example that isn't working?
Our match code wasn't attempting to match the private track secret key within the private track URL and therefore it just fell over. We've changed this now so it should start working as of the next release.
Also, if I cross my fingers and paste the original private URL from post #3 below (https://soundcloud.com/petethomasmusic/boomtown-3/s-KBoVQ) then it should now work: