That is, the add-on would discover one-pixel transparent gifs, take note of what query parameters they used, then every time it found that same gif in the future it would issue a GET with randomly selected parameters drawn from the instances of that same gif it had seen in the past.
For extra crispy electronic warfare, that same add-on could issue GET requests at randomly selected intervals. If those intervals were reasonably far apart (say one hour apart for any one gif) then it would not obviously be an attack on the analytics server.
What it would do is to make it completely useless to correlate your visits to different domains.