Rose seems to be little more than a regular modern day London teenager with a somewhat above average IQ. She has been portrayed as having numerous character flaws (being rash, stubborn, occassionally selfish, often unaware of the feelings of others, and letting her emotions dictate her actions), she has no unique abilities or special powers, she certainly can do wrong (and she doesn't always have justification for it), and she has no distinctive physical features (in fact, her lack of such has actually been the source of complaints). Her name isn't exotic, though admittedly "Russel T Davies" and "Rose Tyler" do have several letters in common (though they certainly aren't anagrams). Her background and attitude seem perfectly in keeping with her peers and where she's from, and as far as we know she's not related to the Doctor or any previous companion.
So it would seem she only possesses a single definite Mary Sue requirement, i.e. being heavily involved in the story... and in my humble opinion, only having one requirement simply isn't enough to qualify a character as a Mary Sue
.
Even this requirement can be debated; I mean, I'd hardly call any Doctor Who companion a "secondary character". Just because the name of the show is Doctor Who, doesn't mean the Doctor is the only main character - the secondary characters are the people who only show up for an episode or two, recurring at best (like Mickey and Jackie). If you disagree, and feel that a "secondary character" being heavily involved in the story is enough to make that character a Mary Sue all by itself, then a vast number of previous Who companions have been Mary Sue's as well, especially Peri and Ace.
Further more, both Russel T Davis and Christopher Ecclestone have stated that if anyone has recieved aspects of Davis' personality, it's the Doctor. After all, what Doctor Who fan dreams of being a companion, when he could dream of being the Doctor?
Incidentally, if anyone in this series of Doctor Who
is a Mary Sue, it's Captain Jack Harkness
.