They would be choked out by weeds long before a second self seeded harvest could develop. Weeds take over very quickly. Most food plants wouldn't have a chance. Even if they did manage to grow without human intervention, much of it would be destroyed by deer and cattle which will become prolific in number and wild within two generations (two to four years).
Eric
No problem Eric, I'm not a vegetarian.
Seriously though, we would be talking very small numbers of people going on the TV scenario, so I think enough of the food crops would survive to feed a small group.
When the first farmers started harvesting they didn't worry too much about the weeds. They used a device which was like a big comb to pick off the seed heads and leave the weeds behind..
If someone has a link showing this I would like to see it please.