I think that today's teens do, in a sense, travel on Damascus Road in many ways, and kind of resembles how teens today are coverted. Paul's conversion, for example, was sudden, expected, and maybe even a little intrusive. I know many teens today who see the light at many unexpected times.
An example would be through the Antioch retreats that I go on at my Church. I know many people who have gone on a weekend retreat only becuase they had to as a requirement for Confirmation. As the weekend(s) progressed, I saw people change from just being there because they had to, to opening up to others and really getting involved about what was going on. Then, every week, the youth group has Wednesday night meetings, so people can continue to strengthen their relationship with God and learn more about Him.
A friend of mine came on a weekend with me because she had to for Confirmation and I wanted her too.
She really didn't want to and thought that it would be a waste of a weekend, she would rather be at the big party that weekend, or at the movies, not After about an hour of being there, I noticed that she changed from acting like she had to be there to opening up and really wanting to get involved and meet new people. I asked her what made her change in that hour. She said that she felt so comfortable with people of her age that she could interact with and share her opinions about religion and God with these other people, and in return hear what they had to say.
Another way of unexpected conversion is if someone close to you gets sick or is close to dying. You might pray to God and say...