The concept that "extreme" experiences bring people together in extraordinary ways is certainly true. I have had this happen to me several times in my life. One significant example will do:

In Basic Cadet Training at the Air Force Academy (called BCT, or the "Beast"), I went through what was probably the most intense and difficult six weeks of my life. It was hell. Or I imagine hell is similar. For us "basics" the only thing we had was each other. This intense experience, where we absolutely HAD to rely on each other for mere survival, bonded all 28 of us in an incredible way. I know each one of those people's first, last, and middle name and their hometown to this day (we had to memorize them) and most likely always will. There exists a bond between us all that will probably last the rest of our lives.

However...

I disagree with this statement made by Extreme Peace Missions:
"...nothing connects people better than the shared experience of facing and overcoming a challenge."

For however great extreme experiences are at connecting people (i.e. my example above), there is still a greater connection. And that is Jesus Christ. For the community of Christ a bond is made and exists that will last far, far beyond this life. I said above that I will have a strong connection to my friends that I went through Beast with for the rest of my life. That is true. But I will have a strong, deep LOVE to my brothers and sisters in Christ, not just for the rest of my earthly life, but for all of eternity. The bonds our creator builds are lasting.

While shared extreme experiences may be an effective tool in peace work, the ultimate answer is people becoming captivated by Christ, not scaling a mountain.