As an amateur triathlete, I feel strongly that running does improve my riding.

First, the physical benefits of running push my respiratory system and help me increase and better understand my cardio limits. When I'm pushing hard on a climb, I feel that I have a better grip on my cardio fitness to sustain a powerful climb the entire way thanks to running.

Second, running has powerful psychological effects. I HATED running. HATED it. Passionately. When I decided I wanted to take on the challenge of 70.3 Ironman, I knew I had to overcome this. I started by literally running 2km over 15 minutes on a treadmill. Awesomely pathetic. 4 months later, I do 2-3 10KM treadmill runs at 12km/h, and I do at least one 21km run each week. I truly love it. I love how I have overcome something I truly sucked at. That experience has transformed me in more ways than just as an athlete.

Go easy when starting out, listen to your body, embrace and effective warm-up and warm-down stretching regimen, and find shoes that truly fit you (For me Brooks Ghost 5 are where it's at) and running can make you better at anything. Period.