In regards to your other thread, I think it's more than possible to ride a century without a whole lot of training. But the event itself is more fun if you've prepared. Kind of like the SATs. Sure you can take them without having studied a day in your life, but you're not going to like the college you get into. (And yes we all know one or two geniuses who never studied ever and took the SATs hungover and bleeding and still got every question right - I'm talking about normal people.)

So it might be a good idea to get a few miles in your legs before doing a century. It's a more enjoyable ride if you prepare.

And as to reasonable shape. If you can walk or go hiking for a few miles, if you can play a pick up game of basketball without passing out, if you can run up stairs with ease, you're in reasonable shape IMHO.