USNA's IT department is far more worried about the network integrity than "illegal or indecent stuff". With that being said, IT IS possible to see who's doing what. But, USNA does not search for illegal activity or indecent stuff without having a just reason to do so....
Think about it, there are 4000+ Mids (and computers) and I can garauntee that many (ok, a lot) look or do things they are not suppose to. When I say a lot, I am talking about a few hundred. They are not going to fry everyone for looking at indecent stuff, but something that may be illegal in the civilian side of the world (such as downloading illegal music) is taken a little more seriously.
With that being said, I am not justifying it is "ok" to do these things (and I don't), but rather answering Zap's question.
The only chat software that I know of that is not allowed is Yahoo! Messenger. DoD has put a block on their port. AOL/AIM/MSN is. Some company's DO NOT allow plebes to use these chatting services (usually just 1st semester or 1st 6/12 weeks -- i.e. based on academic grades). As wheelah44 has mentioned, this rule is commonly broken by plebes.
Word of advice, if you are going to attempt to break this rule (if applicable to your company), do not post your IM name on the facebook site. A smart company took all the plebes IM names, added them as friends, and then asked who had been on (obviously they could tell)...all I can say was big trouble!