I am a serious triathlete, and I resemble (I mean resent) some of these generalizations, but...

I try my best to dress and look like a roadie in group rides. The local bike club will not allow a tri bike in a group ride because they claim (I don't have a tri bike so...) they are dangerously unstable with anyone at the controls. I have thrown the BS flag many times, but it just doesn't matter. I have ridden with many people on tri bikes and they don't do anything any worse than some of the Sunday morning regulars. Show up with areo bars and you will get the third degree, whether they are on a true tri bike, or just clip-ons on a Giant. With that said:

I can run (and swim twice a week) most of the fall, all winter, and most of the spring, ride my bike twice a week starting in March, then go to riding the bike 4 times a week and running 3 times a week in May, and by late August wreak havic on most year round serious bikers. Running helps road biking for the same reason that a tri bike helps a triathlete - A road bike and a runner use a lot of the same muscles. A tri bike is made so that the muscles used to bike are different than the ones used to run, saving them for the run.