Well, you can! How do I know? As someone who took more than a few weeks to even get to a basic level of fitness before I could even start week 1, I have just come back from my first 50 minute run AND ENJOYED IT. I only did about 6.3k in that time, but it took in hills and running through town where people could see me.and the best thing was, I wore my heart rate monitor, and even on the hills my pulse didn't go above 170. I am still in awe of the fact that I can run. I wonder if that feeling will ever leave me.
But if I can do this, almost anybody can. Oh, and I've signed up for my first 10k at the end of June.