It turns out Koizumi's hot springs trip in this series is based on the one in Haruhi-chan Vol. 5.
To (kinda) sum up, while Koizumi is gone on an Organization office getaway, Arakawa turns up wearing a very poor Koizumi costume but entrances and convinces everybody in the club, school, and neighborhood. One of the first followers he wins over is Mikuru; he praises her tea making with such gentlemanliness that she evolves from "clumsy maid" to "chief maid", complete with glasses.
Koizumi-kun!Eep!?UhThe tea is ready sir!Thank you kindly......Asahina-san?UhAsahina-san was, in fact, lonelyAh, youth*squeeeeze*