No you don't.
For one, you're not hosting the content (seeding) like you are with torrents. Claimants aren't generally concerned about the people downloading, they go after the hosts.
And two, you are establishing an encrypted connection to a usenet server which you are then downloading through. Because that traffic is encrypted (like it would be with a vpn), it can't be inspected for illegal/copyrighted content (though that's incredibly rare, ISPs have no incentive to inspect your traffic like that, torrent or otherwise).
Usenet at its core is just an old message board system. People have uploaded files to those message boards by splitting them into small parts and posting the compressed plaintext of each file part into a message on a usenet server. You then read/download each of those posted messages, decompress them, then reassemble all the parts to get the original file. (this is all done automatically by your usenet client and an .nzb file telling it what parts to grab in what order).
Copyright claims can still be filed/submitted, but they go to the usenet provider and are their responsibility to handle and takedown content, not yours as a user/customer.