Of course they can and did, just as many youth groups did before them. This could be your youth group. It's amazing to see the youth of your church getting involved in missions. Youth usually feel more free to minister in the missions environment.
Leaders are surprised to see how involved their youth get.
It's always the ones that you least expect, that get the most out of it. Missions work can super fuel your youth group. It lights a fire in the hearts of young people. Many will see the humble nature and great spirits of the people, and get the desire to serve others no matter where they are at. Take a look at these pictures of previous youth missionaries.