Absolutely not, unless you take "atonality" to mean serialism, which is most decidedly dead as a style.
Many, perhaps most, living composers of serious concert music work within a style that is more or less wholly atonal. Including those who only partially incorporate atonality into their works, that's almost certainly a majority. Granted, many of these are old-guard modernists like Milton Babbitt or Pierre Boulez, but many are also not.
As for the future, I think tonality and atonality will continue to coexist as they do today, at least as far as art music is concerned. Atonality is a technique rather than a style, and is no more a period in itself than is tonality or modality. Therefore, it will not go out of style simply because it has been in use for a century, although specific atonal styles undoubtedly will (think about the decline of twelve-tone music in the last thirty years, for instance).
And goodridge_winners, atonal music doesn't necessarily need to be avant-garde. Many composers (Ralph Shapey and Shulamit Ran spring to mind) have combined essentially non-tonal languages with very conservative forms and styles. And isn't it a little arrogant to claim that something "isn't music" simply because it doesn't appeal to you? There are many composers and individual pieces I can't stand, but I've never believed them to be non-music simply because of my dislike for them.