No, the data for Connections is not stored in a CPT. Connections is actually older than that feature in WordPress. I had considered migrating the data over since the schema partly overlap, especially the taxonomy and meta tables, and I could take advantage of core WP features to accelerate development. But I did decided against it because the post db schema just is not a perfect fit and so it would actually get in the way of many of my future plans. Then there is the performance aspect. Many Connections users have many thousands of entries in the Connections db; upwards to 40,000 in one instance. That would mean that user 40,000 extra “posts” in that table and the then postmeta table would absolutely massive to the point I could not even begin to guess. Some of the queries I already do simply wouldn’t perform well. Of course the downside is I have to work hard at adding functionality that I could have leveraged in the WP core for CTP. Honestly, I still go back and forth on this issue.
Now, to actually answer your questions…
I do have plans on implementing a way to create custom taxonomies but I could tell you when those plan would come to fruition. But my plan do include the possibility of doing exactly what you’re asking.