Are the TRC brass pens interchangable?

Hi everyone, I recently got myself a passport TN for my EDC and have been looking for a proper pen to go with it ever since. I am desperately in love with the limited edition Tokyo pencil and am wondering whether I might be able to also get the brass ballpoint pen and then swap the cover (or casing, whatever you'd call it), so I could use it with my TN.

Does anyone know if the ballpoint tip might fit into the pencils casing? It would be lovely if someone could try that out for me. 🙃