Joseph: I don’t know if there is a “typical” path. One of my son’s learnt in the Beis Medrash of the Yeshiva where he went to Mesivta. His “American” RY suggested that he and some other talmidim would do well in EY and made all the arrangements to have them accepted to a certain yeshiva. They all learnt in EY for 2-3 years. My son came back for one zman to BMG, was redd a shiiduch that was B”H successful and has returned to his yeshiva in EY.
Another of my son’s also learnt out-of-NY for High School and went to Beis Medrash of the Yeshiva where he went to Mesivta. He then returned to NY and learnt in a Yeshiva in Queens (not Chofetz Chaim) for 3 years and then was hired by an out-of-town yeshiva as a dorm monitor/tutor.