I saw a halakha (maybe in the Maharil) that says that the chazzan on the yamim noraim should try to cry or at least sound as if he is crying when leading the tefillot on such days. Wailing sounds, I suppose, are seen as appropriate and effective on these occasions.
Certainly, much of the Ashkenazic nusach sounds mournful and tearful (even on a Yom Tov), such as for the piyut Le El Orekh Din. In this vein, it would then be appropriate for the hatah to cry. I know that should HKBH bless me with finding my basherta (Please, G-d, may it be soon!), I’d be emotional under the huppah.