Everyone would love to travel and would travel and if they had the opportunity or money and time to do it.
Church elders of a global church may travel plenty enough to different countries to check on their churches. Popular pastors also gets invited to preach in many different churches in different countries. However, you don't get to be a church elder or popular pastor right out of college UNLESS you work as an assistant or secretary, etc, for a church elder who travels a lot.
Working for a global church organization would definitely improve your chances of getting a spot for good travel opportunities....But, big, 'mega churches' tends to have questionable theology / doctrines. Greater likelihood they are spreading false teachings. We live in an evil world where the devil is god so churches and pastors who (even if unknowingly) preach false teachings gets the chance to be huge and popular, blessed by the devil himself.
Churches / organizations who engages in humanitarian relief may also get you good travel opportunities especially if you're a doctor. There really isn't much opportunities until you've gone up the ranks, become popular or a doctor in field medicine.
Missionaries get good travel opportunities but not always. Within a big church organization, a missionary pastor may get invited to their other churches in other countries as guest preachers but you don't usually get these opportunities until you have spent many years within the church organization. A church org that is still small, only few church sites may not award much travel opportunities even as a missionary.
