Yeah, Link is a character, but not quite in the traditional sense. Each incarnation of link has a certain amount of character to them, some more, some less, however the over-all-incarnations link is also a character. In some ways, its like the Avatar in the animated series. Aang is a character. So is the Avatar as a whole though, there are certain facts about them that make them the Avatar. No, in that show gender is not one of them, since the spirit being passed along is giant-good-spirit-squid-goddess-thing instead of necessarily the first Avatar's spirit. Link is a character in the same sense, or I guess the concept of link is some level of a character, and one could make the case that it is by-necessity male, as its the reincarnation of the male hero who saved the Goddess Hylia or W/Es spirit over and over, whilst Zelda is the reincarnation of the Goddess Hylia, and Ganondorf is the Reincarnation of Ganon over and over, and they are the same characters, repeating the same story, over many generations for all eternity. That said, they could also easily insert a bit of lore that allows Link to be female sometimes.
It also depends on which timeline and game we're talking about, and where its set. For example, Wind Waker went on to immediately become Phantom Hourglass, and kid Link was used in both games. Doing something like that, then suddenly allowing a change of gender would be... weird. Same for OoT and MM. Not sure, haven't played them, but I think the Oracle games were similar. And then in a Link Between Worlds, it mentions Link from a previous game marrying the princess or something in some murals at the Royal Palace, if I'm interpreting them correctly, and that sort of reflective thing couldn't be done if you don't know the gender of the hero.
Overall though, yes, Link is a character. Both the individual Links themselves, even if they're not always the most characterised outside player actions, but the concept of Link in-universe as well. Doesn't necessarily exclude a female Link, but at the same time it doesn't really immediately allow one either.
In any case, its Nintendo's game, they can do what they want with it, and so long as the gameplay - Zelda's strong suit - is good, and its story isn't horrible, the game will probably do fine.