No, I don't think so.
I'm a better driver AND a better bicyclist because I ride a motorcycle.
Riding a motorcycle taught me a lot of the things others have mentioned - lane positioning, seeing with my whole eyes, avoiding target fixation, body steering (ok not relevant to cars

), eschewing distractions. When I came back to bicycling, I brought those skills back with me. I'm not sure I ever would've learned how to see at 70 mph by riding a bicycle at 20. I guess that's where MTBing might help (obstacles being closer means they appear to be coming at you that much quicker), but I never did much of that.