I don't do Iaido, although I've had superficial brushes with it for many years (plus I stayed at a Holiday Inn Express!). I don't do Shodo, traditional Japanese dance, Tea Ceremony, Kuroda Sensei's sword style, DR, etc., either, but I can tell you that all of them have aspects of the ki/kokyu skills and those skills are, as I've said many times, the essence of the "hidden" teachings in many Asian arts. I watched a video about a year ago of a well-known Iaido expert (old man)... and he definitely used those skills. Most Iaido I have seen otherwise has not had those skills.
Not that I want to get into another discussion about the ki/kokyu skills, but I did want to make a nod toward some of the posts to the O.P. about being careful to get a qualified instructor. I think it's harder than that. There are "qualified instructors" in all the arts I listed above and many of them have various licenses and diplomas, know many "subtleties", and so on... but they don't seem to have the basic ki/kokyu skills.
Although it's not about Iaido, this interview with Seiseki Abe about using "kokyu" in Shodo/calligraphy, kotodama training, etc., is relevant not just to calligraphy, but to Iaido and other arts as well. All of these things penetrate the arts and are interconnected: