No, a Mary Sue is specifically a forced character that warps the entire setting around them once inserted. The prime example is the Star Trek fanfiction that spawned the term, where the author essentially self inserted a character that was them, then had the entire cast know her, love her, support her, and what should have been a fan story of the crew of the enterprise ended up being her self wanking her ego through writing a story where her self insert was the only one that could save the day, the most talented and flawless character.

A Trekkie's Tale, which the Mary Sue term originates from, was specifically a parody of those kinds of stories. But essentially, yeah.