There is a din of "amor lahem" in birchas kohanim that requires the kohen to articulate the bracha. The Beis haLevi writes that there is no din of shomea k'oneh by birchas kohanim-- it must be spoken and heard (Chazon Ish disagrees.)
In Rav Shteinman's sefer Ayeles haShachar on the parsha 6:23 he quotes a first hand account from someone who learned by the Chofetz Chaim when the yeshiva in Radin was first started. The CC had to travel to Warsaw after Pesach to take care of the publication of the Mishna Berura and en route, he remarked to this individual that he was worried about being stuck over Shavuos because he was mesupak how to recite birchas kohanim in Poland: must he pronounce the words in Polish accented Hebrew, the way everyone else in Warsaw speaks, or can he pronounce the words in his Litvishe accented Hebrew? Apparently the CC assumed that the bracha being spoken means pronouncing the words the way everyone else does.
The individual relating the story added that he quoted to the CC from some unnamed sefer that claimed that the Polish pronunciation was erroneous and should be disregard, but the CC paid this no heed. Later, he learned that the author of the unnamed sefer (any guesses?) was a maskil and that's why the CC, he assumes, ignored it. Rav Shteinman then adds icing on the cake and claims that he heard from R Zak's, the CC's grandson, that the CC would often deliberately mispronounce the word "atah" as mil'eil instead of milra "l'hotzi mi'lev hamaskilim."
So let me get this straight: the CC deliberately introduced errors into the way he pronounced words in davening just because the maskilim were the one's doing the right thing? Since when do we deliberately do something wrong "l'hotzi mi'lev...?"
End of the story: the CC duchened using the Litvishe pronunciation. Adds R Shteinman, it is well known that the Litvishe pronunciation is close to the Teimani pronunciation.
Not sure what he means by that final comment. Does R Shteinman think the Yemenite pronunciation is most exact and therefore whatever is closest to Yemenite is more correct? So why not simply duchen using the Yemenite havara? Or does he mean that since the Litvishe and Yeminite pronunciations are close (are they really?), it is like having 2 eidim that they are the correct havara? Should we all make sure to read krias shema in a Teimani or Litvishe accent to make sure we are pronouncing the words lichatchila correctly?