Varley, H. Paul, and Kumakura, Isao: Tea in Japan: Essays on the History of Chanoyu, pp. 13-14.Rules known as shingi were established in these [Zen] temples and became the basis for a form of communal life that governed the typical day of the priests […]. A work dealing with shingi that exerted great influence in Japan was Ch’an-yüan ch’ing-kuei by Tsung I of the Sung dynasty. […] It is said that, as a result of the Sung-style rules he [Lan-ch’i Tao-lung (Rankei Dōryū)] codified at Kenchōji, rules were established at Zen temples throughout the country. […] Insisting that the procedures for the Zen sect must be entirely in accord with those of China, he [Ch’ing-cho Cheng-ch’eng (Seietsu Shōchō)] reformed the rules of the Zen temples of Japan. […] Among these shingi were rules dealing with the drinking of tea (that is, sarei). […] In this sense, chanoyu emerged from the sarei of Zen.
So of course I’m not saying that these monks practiced chanoyu, but there does seem to be a connection in that you probably wouldn’t have chanoyu without Chan/Zen Buddhism…?