I was under the impression that the term counter tenor referred to singers who had trained their falsetto voice to be powerful enough and to have sufficient range to cover much of the music written for castrati (and of course the twentieth and twenty-first century music written especially for the counter tenor voice). I think of Alfred Deller as the pioneer of this voice type on stage (though I believe it was common in English church choirs before then).
With this definition adult male sopranos or trebles whose voice never broke are not countertenors. Perhaps a similar question is whether castrati are counter tenors, and I think the answer is clearly "no".
Are adult male trebles counter tenors?