No, Burnham is not a Mary Sue.
She is not an obvious surrogate/stand-in for the writer/producer who shows up one day and upstages the regular protagonists, whom everybody falls in love with, and who always saves the day in implausible fashion and can do absolutely no wrong. People are forgetting what the term "Mary Sue" actually means, and just throw it around like a Lacrosse ball for "any character I don't like."
Kor
She is not an obvious surrogate/stand-in for the writer/producer who shows up one day and upstages the regular protagonists, whom everybody falls in love with, and who always saves the day in implausible fashion and can do absolutely no wrong. People are forgetting what the term "Mary Sue" actually means, and just throw it around like a Lacrosse ball for "any character I don't like."

Kor