I agree with Mr. Governo, that self-insertion in somebody else's milieu is the characteristic property of a Mary-Sue, and with "rahullak," that even though the trope originated with a character created as a parody of bad writing, it doesn't necessarily follow that a well-written Mary-Sue character can't exist (and indeed, I regard Piper as a defining example of a well-written Mary-Sue).
I might add that there can be no more blatant evidence of self-insertion than having the entire story told in first person, in a milieu where every other officially authorized story (or very nearly so) is told in third person.
As to Calhoun and the whole New Frontier series (and Gold and the SCE series [and I, for one, would like to see the rest of that series available in hardcopy], for that matter), and other series that didn't originate in produced screenplays, I don't really see them as Mary Sues (or Larry Stus), because they aren't author insertions, so much as they're separate sub-milieus, the same as TOS, TNG, DS9, VOY, ENT and the Abramsverse are effectively sub-milieus. Ditto for Mr. Cox's books about Gary Seven, Khan, Shaun Christopher, and Mr. Bennett's books about the DTA; they revolve around characters that are already (if only by reference, in Shaun Christopher's case) canonical, but merely underexplored in canon.
Ford's How Much for Just the Planet,
of course, is a veritable author- and friend-insertion festival.