You can tour without training, but you will enjoy it much more if you are in shape for it! I ride in supported tours almost every year, and there are always people along who do little or no training. They manage to ride 60 miles or so every day like everyone else. However, they are the last ones to finish riding every day, sometimes not reaching the destination until it's almost dark. They are also the ones who get saddle sores, have mechanical problems with their bikes and get rides from the SAG wagons when available.

For me, training is not a problem because I like to ride. So I bike commute and ride recreationally year-round. It is not a chore, it's my hobby. I don't think I would enjoy bike touring if that's the only time I rode.