Piracy: ꜱᴀɪʟ ᴛʜᴇ ʜɪɢʜ ꜱᴇᴀꜱ

If you're taking part in transmitting a torrent over Yggdrasil, then people you've peered with in the swarm will definitely see your Yggdrasil IP - which is based off of the encryption key you generate (and you can change whenever you wish) for the connection to the mesh.
Regarding obfuscation of what you're accessing inside something like the bittorrent DHT, that could likely be done with multiple Yggdrasil connections and torrent clients - so each address only associates with one torrent, it's just not a core feature of the network itself.

The Yggdrasil network really isn't meant to provide perfect internal anonymity between two directly communicating peers, it's instead built to be an easy-to-use, end-to-end encrypted, mesh network - with great performance.
It's there to protect the content and target of your communications from anyone beside you and said target, without adversely affecting the delivery of said content. Not to protect you from your communication target, though it can do a passable job at that too.

My main use of Yggdrasil has actually been as an easily setup alternative route into NATed systems, seeing as I can easily hit 600Mbit and get below 15ms of latency over it, which I quite often use to run VNC or SSH (and SCP/rsync) over. And since the mesh can be established as long as you can reach a node, it becomes ridiculously easy to get a functional link over it.
Transmitting DC++ traffic without my ISP being able to detect any of that is just a bonus.