You need to go into commerce if you want exposure to management experience. I did ACCA first and then jumped ship and did CIMA and have just started my IIA (Institute of Internal Auditors) exams as well.
I haven't actually done any real accounts work for over 4 years now as I specialize in SOX work as I find it more enjoyable for some reason.
CMI is a good way of gaining the theory but you need the experience to back it up and the easiest way is by making the move into commerce. (plus the pays better).