How would the "parody" work? People have used the characters, settings, plot devices and so forth of other fanficcers countless times (with permission from the original author, of course). That's perfectly fine. We've had some issues with other forms of parody, though, especially those that were especially critical of the original (such as MST fics).

As long as you're not flaming the original work, it's usually okay - with permission - but if you're using your piece simply to say "this fic sucks!" then it could be a problem. I and the other mods would likely have to discuss anything on that end of the criticism spectrum.