IO
To start with, there has been assorted cases of WGA saying that genuine MS software is "fake". Another problem could be that your serial key has somehow been compromised and used by someone else, someone using a hooky version of XP where they have used a keygen to get a serial number is one example of that.
Now, would the key be accepted whilst "online" to MS? Yes, although I wonder how you were online while installing windows as the key's only asked for during the initial stages of the install before anything like drivers are installed...
Certain updates are downloaded before the WGA, so you getting some updates is normal. You can remove the WGA, and when you update windows you can "deselect" it so it doesn't get downloaded (I assume you mean the WGA tool, and not the WGA check on Windows Update which cannot be avoided.) so it doesn't bother you again.
Now, to WGA itself. It won't check anything else apart from Windows. Office has a separate validation programme (Office Genuine Advantage) which you have to download/install when you first update office. The WGA only checks your serial key, to make sure it is a "real" one/isn't installed on 20 computers instead of one/etc. That's all. Let's just say that because of that check both the WGA and OGA are easily circumvented.