It's more like three blocks, and that is from the western edge of the hospital. In my experience, hospital workers just do not stray very far from home base at all --- their breaks are just too short and they have other options.
Re: on the way in or out and the 24 hour thing, I buy that to a degree for sure, but it would be a more powerful effect if it was like a coffee or fast food drive-thru.
All of this said, I am sure that there will be hospital-related business and there are a lot of non-hospital medical buildings in the area, including one right beside the new store.