(Literally) any experienced teacher who does pronunciation well believes in the centrality of rhythm to fluency, and probably much more, including memory and perceptual processing. The "problem" has always been that the best arguments for rhythm-based practices have been experience or affect (motivating or promoting "flexibility" in some sense). The best evidence today still comes from parallel fields. For example:
"We think this could extend to interpersonal synchrony in other fields, such as recreational activities like jogging, where health benefits may be greatest when partners are matched for rates; or in education, when teachers and students are matched in conversational speech rates; and especially in sports, such as tennis doubles, pairs skating or team rowing," (Emphasis, mine.)
Previous studies reported here and elsewhere have established that ability to move to a beat and perceive rhythm (but not simply tapping it out or clapping hands to it) seem to enhance skill or language engagement and acquisition, especially in children. The question, of course, is if, how and when adult learners (in class) can arrive at that synchrony and whether or not such coordination is more "innate" to individuals or can be taught. Lessac clearly believed and demonstrated the latter. Morley and Gilbert see L2 rhythm as developing alongside or conforming to the L2 more gradually, or implicitly.
Whichever approach you take--and haptic pronunciation teaching is very much on the Lessac end of the continuum, requiring synchrony of body movement and rhythm continuously in instruction--to quote one of my father's musical icons (Duke Ellington): It don't mean a thing, if you ain't got that swing . . .
Gilbert, J. (2010). Clear speech (4th ed.). Cambridge: Cambridge University Press.
Lessac, A. (1997). The use and training of the human voice: A bio-dynamic approach to vocal life (3rd ed.). New York: Drama Book Specialists.
Lessac, A. (1984). Body wisdom: The use and training of the human body, New York: Drama Book Specialists.
McGill University. (2016, February 9). Find a partner who marches to the beat of your own drum: Group coordination is optimized between people with similar movement rates. ScienceDaily. Retrieved February 25, 2016 from www.sciencedaily.com/releases/2016/02/160209121726.htm
Morley, J. (1997). Improving Spoken English: An intensive personalized program in perception, Pronunciation, Practice in Context. Ann Arbor: University of Michigan Press.