The answer is no, and it drives me nuts. I have no idea what BMW was thinking. I can understand the transmission not defaulting to sport, but I have mine programmed so just the suspension is firmer in sport mode. Just one of a long list of BMW stupid quirks that detract from such a great driving car.
GONE: 2012 BMW 550 M-Sport
2016 Audi A7 Prestige
2016 Lexus GX 460---Wife's car
2015 BMW 1600 GT---2016 BMW S1000R---2012 Ducati Panigale