Depends on where the server is located.
In the US, usenet servers have been under 'common carrier' laws and provisions for a VERY long time, just like the telcos (internet carriage by the cablecos is rather recent, and there is some question there as to common carrier status).
By saying that, they are completely immune to being sued, although there is some question as to DMCA provisions which may (and some parts of it already have) been found by the courts as going against the common carrier laws (over 150 years old).
In other words, just like the telcos can't be sued for 'carrying' 'perhaps' illegal messages (up to and including bomb threats, for instance), they can't be held accountable for anything else.
Now, IF they can obtain records, or 'tap' your line (another hazy part of the law in the US at present), is another thing. Obviously, if you use SSL, it's remote/impossible.
Some usenet server operations have been 'erroring on the side' of the DMCA, although again, it's 'hazy', and have erased files on nothing more than a 'takedown' letter from the *paa's. But that's just one server, and there are dozens.
I would venture to say that any server operations that 'gave up' the uploader (name, ip, etc) would be out of business the next day.