I also read this question to be asking if those who have an entry in any of the Great Migration series (by Robert Charles Anderson) should have a category. They do this over at WeRelate. See Great Migration Study Project
Currently there are two categories related to these immigrants, although WeRelate does not distinguish them for purposes of the project above.
1. Mayflower (Pilgrim separatists); wikitree Categories here include:
a. Mayflower (passengers only)
b. Mayflower_Project (passengers and their descendants for many generations)
2. Puritan Great Migration (Puritans who fled or were kicked out of England before the English Civil War); wikitree category Puritan_Great_Migration
AND there are also currently two series by RCA:
1. Great Migration BEGINS (1620-1633) - includes both Mayflower Pilgrims and the later Puritans
2. Great Migration (1634-1635) - mostly Puritans (as the Pilgrim emigration had ended by this time) and other non-aligned emigrants
So... how best should we be categorizing the appropriate profile pages?