Is Rey, From The Force Awakens, A "Mary Sue"?

I'm a Star Wars fan and I very much enjoyed Star Wars: The Force Awakens. If you've seen it and engaged in any critique of the film, you've probably heard the character Rey referred to as a "Mary Sue". Here is the definition of Mary Sue, as defined by Wikipedia.

"A Mary Sue or Marty Stu is an idealized and seemingly perfect fictional character. Often this character is recognized as an author insert or wish fulfillment. Sometimes the name is reserved only for women; but more often the name is used for both sexes."

Since Rey quickly learns and applies her "Force" abilities in the movie, people gawk that she did not "earn" that character development and as a result, refer to her as a Mary Sue. I beg to differ.

While I was watching the scene early in the movie where Rey marks the wall for each passing day (See Above), in my first viewing of the Force Awakens, I realized Rey had already completed the hardest part of her force training and neither she nor most audience members realized this. It excited me because I knew she was bound to do great things through the remainder of the film.

Without any family, she learned to survive. As a result, when we meet her she is focused and disciplined. She constantly sought to learn and explore. She held onto a strong sense of faith that her parents were coming back for her with no evidence to support her belief. These are difficult to master attributes, and she did it before her true journey even begun.

Now contrast this to Luke Skywalker. When we meet him, he’s undisciplined, easily distracted and a complainer. He lacks a meaningful amount of faith in the force as demonstrated by his training with Yoda, in the Empire Strikes Back

So no, Rey is not a Mary Sue. Rey paid her dues and did her training preparing for her return home only to realize it would turn out differently than she expected. She will need to learn how to channel her focus and discipline from and through the force but, like we saw in the remainder of the movie, it will go fairly quickly.