Tom
Istar
Then I imagine it would no longer fit the description of Mary Sue.
Exactly. The difference between Mary Sue and unreliable narrator is that the Mary Sue is upheld by the author as perfect. He or she can do no wrong, there are no consequences to his or her actions, he or she is often ridiculously overpowered and inexplicably good at everything, and characters who don't like the Mary Sue are either punished, shown to be total idiots (or evil), or are converted by the Sue's sheer awesomeness. Often something happens in the story to prove to everyone that the Sue is the most Speshul and amazing character. I like to call that "Word of God", since I can just see the author in the background, going, "See? See?! Of course he/she's the best!"
In my opinion, the Mary Sue trope is defined by its lack of self-awareness. A Mary Sue's author doesn't know (or want to know) that their character is unrealistic, and often gives the Sue faux flaws to prove that he or she isn't perfect.
If the author is aware their character's too perfect, they're either setting that character up for some massive development, or are playing the Sue trope ironically. I've done that a few times myself; it can be fun.