Divrei Chaim blogspot bases his words on Rabbi Wahrman. He says, there is a well known machlokes between Rashi and Tosfos (Brachos 21) regarding what to do if one is in the middle of shmoneh esrei and the tzibur is saying kedusha. Rashi writes that one should remain silent and simply attend to the recitation of the tzibur -- based on the principle of shome'a k'oneh, hearing can substitute for actually saying the words. Tosfos disagrees. If hearing is equivalent to saying the words, then listening to the words of kedusha would be no less a hefsek, an interruption, than actually reciting the words themselves. According to Rashi, obviously this is not the case -- there is a distinction between a recitation done aloud and recitation done quietly or by listening.
He then goes on to explain why "Baruch shem..." that we say after the first Posuk of Krias Shema is not a hefsek. Based on the Tzlach , he suggests that there is no problem of creating an interruption because we say, "Baruch shem..." quietly. “In other words, a quiet recitation, a recitation that is different in tone than the normal tefilah voice, (my emphasis) does not constitute a hefsek.”
"This is exactly the point Rashi and the Rokeach were making. Through shome'a k'oneh listening counts the same as a recitation of kedusha, but since that recitation takes place silently, it does not count as an interruption."
Perhaps we can extend his idea a little to include the humming.
On the other hand, at least for the first brachah of Shmone Esrei see this
OC 101:1. “In addition, one must not think other thoughts during the first brachah of Shmone Esrei, even when not actually saying the words. According to some poskim, those thoughts may constitute a hefsek which may invalidate the brachah - see Mishnah Berurah 63:13 and Biur Halachah 101:1 quoting the Rashba and Igros Moshe OC 5:5.”
It’s a clear CYLOR.