The question asks for studies or research, and I don't know of any, but I do have some first-hand experience.
Meeting the Section 508* requirements for Web pages used in such a course is effectively without cost if one starts out to make such pages accessible. Retrofitting might cost as much as the original project, but the cost should be near zero for modern MOOCs.
Closed (or open) captions are very expensive. Unless done at a foreign sweatshop, cost is $5.00 to $15.00 per minute, so something like $12,000 as a minimum, up over $35,000, for a one-semester course. In other words, the captioning can cost more than the professor. That's at least part of why some institutions employ ASL interpreters for class sections with deaf students.
Edited to add: I worry about the quality of the content for captions of university-level courses produced offshore at cheap rates, but have no personal experience. I have experimented extensively with captioning through voice recognition for my own courses. It's getting much better, but still requires extensive manual editing. The $5-15 number given above could be reduced by using student labor, especially if the students are majors in the material being subtitled.
Captioning addresses the needs of the deaf. Making course materials available to the blind means being sure that everything that is shown is also described, either by the speaker who is presenting or in a manner that can be rendered through text-to-speech. The latter means being sure that there are good "alt" descriptions of images and that appropriate markup, e.g. MathML, is used for things like equations. In my own discipline, computing, that isn't onerous, and the costs sort-of disappear in the weeds of getting the course done. Things might be very different in a discipline like the visual arts.
*Section 508 is part of the Rehabilitation Act, not the ADA, but you still have to do it.