Then he spends dinner asking Yzma about Kronk ('so he seems nice? He's what, in his late twenties?') and otherwise being slightly obsessed with him. Then there is the whole Adventure of Doom with Pacha, him being ever huffy about the Kiss of Life, and then the restaurant gag where Kuzco takes to playing Pacha's fake wife and dressing up in ladies' clothing with great gusto (reinforced by the waitress' 'bless you for coming out in public' remark when Pacha says they're on their honeymoon). Then when he is finally de-llamafied, we don't see him paired off with the obligatory girl from the lineup earlier, as might otherwise be expected in a Disney movie.
Instead he is still single, but goes to found family it up with Pacha, Chica, Kronk, etc, which dare we remark is a very queer trope.