I'm honestly not 100% sure as I believe the automatic transmission part numbers are different although both are GA6F21WA.
2011 -
RealOEM.com - Online BMW Parts Catalog
2007 -
RealOEM.com - Online BMW Parts Catalog
2011 control unit -
http://www.realoem.com/bmw/enUS/showparts?id=SV33-USA-02-2011-R56N-Mini-Cooper_S&diagId=24_1087
2007 control unit -
http://www.realoem.com/bmw/enUS/showparts?id=MF73-USA-02-2007-R56-Mini-Cooper_S&diagId=24_1087
I've never done something like this myself so I'd probably suggest doing a quick Google search and finding an independent MINI specialist shop in your area or even in the states (not sure what $$ for calls here would cost you) as they would most likely be able to tell you if it's possible. I wouldn't be surprised if a few items would need to be changed from your N14 R56 to be compatible with the N18 R56 transmission.