Skateboarding made me practically slip proof. When I slip on something my body instantly drops a level, distributes my weight evenly on both feet, and I ride out the slide. I did this once on a sloped driveway and ended up having to slide all the way down the driveway while standing, just naturally reacting to the slide so I wouldn't fall.
But yes, with jiu jitsu my sense of awareness is heightened. For example, I'm clumsy as hell but if someone throws something at me without warning I can catch it perfectly. If they tell me they are throwing it, I always drop it. The same thing goes for throwing accuracy.. but I only see the jiujitsu gains when it's automated responses.