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.
2012 BMW 550 M-Sport
2015 Audi A7 Prestige
2014 Lexus GS350---Wife's car
2013 BMW 1600 GT---2011 Kawasaki Ninja 1000---2012 Ducati Panigale