I asked a local dealer if it would and they said they'd find out and let me know. I never heard back from them. Big surprise there.
Won't work on the SE, MINI hasn't offered the "S3ARA Rear Luggage Carrier Preparation" for it. Normal SE doesn't have the second tow hook port nor the electrical port. Probably not offered because of the rear parking distance control (PDC).
You might have to roof mount it on the crossbars or seasucker bike mount (have to remove front tire).
Thanks for the replies. It's a little disappointing as I would imagine a rear mount bike rack would cause less range reduction than a roof mount. I have a rear mount fitted to a 1-1/4" receiver on my Mini Cooper S and it does a great job of carrying 2 bikes.
You could install a trailer hitch like this person: https://www.insideevsforum.com/community/index.php?threads/mini-trailer-hitch.11656/