I gotta agree with GM on this one, but personally I can't see Anna as a series mascot. Hell I wasn't even aware she existed till I came across this thread back in November. I never realized that all of the Anna in the FE games were the same girl. Like, I wasn't even aware they were all named Anna.
To me, it was more like a neat little Easter Egg, than a mascot. It'd be like calling Nurse Joy the series mascot for Pokemon because she's in every game.
If any character is the mascot, it'd have to be Marth.
I'm glad Anna is getting more recognition and she's being fleshed out as a character, and I'd love to see her get more playable roles in future FE titles, but atm, I feel it's too soon for her to be labled as anything other than a neat cameo. Even among FE fans she's kinda unknown, like I said, I've played 7 games in the series, and was never aware that she existed. Likewise consider those who only played 13, if Anna were in Smash 4, they'd be confused as to why a generic unit got in over the likes of Lucina or Chrom.
Personally, I kinda find Anna's chances to be MUCH lower than what people think. If anyone is willing to convince me otherwise though, by all means. I'm just voicing what I think, but if there is evidence to the contrary, then I might join your ranks. I just don't see Anna as important enough to the series to merit a Smash inclusion.
Not over the likes of Roy and Lyn, and especially not over the likes of Lucina.
EDIT:
Likewise, I gotta agree with Diddy that Impa is more important to Zelda than Anna to FE. Impa's had prominent and important roles in several games. Whereas Anna could always be ignored and was the equivalent to say... Beedle, Malon, the Postman, or the Great Fairies. All of them appear in multiple games, and they have similar roles to that of Anna.