Yes, it's s simple swap to put 294mm S discs and pads on the SD, using the calliper brackets from an S - the callipers are the same for both cars and the hydraulics don't need to be touched. If the car is more than ten thousand miles old, getting the disc locking screw out of the discs/hubs may be difficult as they seem to freeze/rust in place. I now remove and re-copper-grease the screws on my car each time I swap from winter to summer wheels and vice versa.
It seems if your SD is a very early production, it may have 294mm discs already - mine was built late 2012 and had the smaller discs.
S discs will fit under 16" OEM Mini wheels, but not under 15" ones.
If this is a mainly visual/boasting improvement (as most brake mods seem to be), don't bother, as the S discs don't look significantly bigger.
I found the S discs cured the appalling brake fade I got with the original 280mm SD discs but did not turn the brakes into something which I could enjoy. I then switched to Mintex M1144 pads and now have no complaints. Whether just the Mintex pads on the SD discs would have been good enough, I couldn't say but in future I would try them on their own as new discs and calliper brackets as well as new pads costs quite a bit.
A low-res photo guide to swapping the brakes is attached. PM me with your email address if you want the full fat version (too big as a forum attachment), though frankly there isn't much missing on the low-res version.