Can't speak for the Mini Convertible, but on my Jaguar Convertible I advise folk against lowering or raising the roof without the engine running i.e. on battery power alone. Operating the Convertible roof without the engine running is a serious load to place on the battery. There is an aftermarket option that does allow the key fob to operate the roof up / down on a Jaguar Convertible, although I obviously have not gone down that route, however if someone is doing it for a Jaguar, then there is bound to be someone doing it for the Mini - its a fairly simple piece of coding.
Jim M