I love running and find myself running a lot more 7 days out from my last drink. It's a release... I don't think it's an addictive behavior. I think it clears your mind and offers solitude and moments of clarity.
That said... I have a friend that runs ultramarathons. It completely absorbs him. He literally runs halfs and full marathons daily with 30+ milers on the weekends... spending hours and hours training. We've all agreed there's something a little "off" with him... =)
I'm assuming if you're looking to tackle a half that quickly you already have quite a bit of training. I'm a regular (when sober) 5 - 7 mile/day... it's been a half as a goal for two years. Maybe this summer... But, if Al Roker can run a full...
Best of luck.