How do you think that having this compact might have affected the Pilgrims once they arrived in North America?

The compact was in effect until 1691 and tried to establish self-government in America, being the first document attempting to do so. The Pilgrims arriving in North America would have "legal" dominance and liberty to settle and bound themselves to this New World. Arriving on September 16, 1620, the Mayflower, a British ship with 102 passengers, was responsible for this document, hence its name.