The gemara says that a kohein can only go up to du'chan when he is old enough to have a beard. Tosafos asks from the gemara in megila which implies that as soon has one is no longer a katan he can du'chan, and from a gemara in succah which implies that even a katan can duchan. Tosafos concludes that there are 3 distinctions. When he is only enough to have a beard he can duchan alone even b'kvius. When he has 2 sa'aros and is no longer a katan he can du'chan alone but not b'kvius. But as a katan he cannot duchan alone. These 3 categories are paskened in Shulchan Aruch 128:34.
It isn't clear whether a katan can du'chan with others even b'kvius. The Biur Halacha cites the O'las Tamid that so long as he is duchaning with other kohanim, a katan can even do so b'kvius, and deduces this from the language of the Shulchan Aruch. The Biur Halacha also writes that in the absence of another kohein, one can appoint a person who is a gadol but isn't old enough to have a beard, even as the established kohein. The rationale would be that technically once he is a gadol he is old enough to du'chan, just that we don't allow him to do it b'kvius due to kavod tzibur, so when there is no other kohein we assume that the tzibur is mochel.
It would seem that a katan is not able to du'chan even m'doraysa just like avoda where the gemara learns out from pesukim that a katan is pasul for avodah. If this is true it would make sense why even if the tzibur is mochel, it would not help to have a katan duchan alone. The only purpose of a katan duchaning would be chinuch as the Shulchan Aruch seems to say. However, Rashi in Megila 24a which is quoted in M.B. 122 writes that the reason a katan can't duchan alone is due to kavod hatzibur. This implies that m'doraysa even a katan can duchan. Therefore it is hard to understand why the olas tamid is only matir a gadol who doesn't have a beard to duchan in the absence of another kohein since we assume the tzibur is mochel, but wouldn't allow a katan to duchan. Since both one who is not ממלא זקנו and a kattan are only not allowed to duchan due to kavod tzibur, we should assume that the tzibbur is mochel when there is no one else?
Perhaps the peshat is that a kattan's ducaning is invalid m'doraysa just like he is pasul for avoda. However, for the purpose of being mechaneich him we should allow him to du'chan as we are mechaneich children for everything. Rashi just means to say that for the kavod tzibur we aren't mechaneich children to duchan. But ultimately, even if a katan would duchan, it would not count. Therefore, the mechila of the tzibbur only helps for a gadol who isn't ממלא זקנו but doesn't help for a katan.
Tosafos (here and more so in succah 42a) implies that ta'aniyos are considered k'vius. Therefore it should come out that one who is not ממלא זקנו cannot duchan alone on taniyos and on yom kippur. The Biur Halacha doesn't understand why the poskim don't mention this.