I don't think the pilgrims were invaders as they were just looking for a new home free from persecution.
The real invaders came under orders from their kings and queens to set up places for their troops and to manage to get any gold and silver items for the enrichment of the crown lands and treasury. They came from several lands in Europe. England, France, Spain, Italy, Germany, Holland, and so forth.
The only one that I remember reading about that did no harm to the Americas and the natives was one of the Nordic countries. Maybe it was Sweden or Norway. The crossed what is now Canada and had settlements as far west as what is now mid Canada and I believe down into Wisconsin area of the US.
No because refugees are fleeing war torn areas. The pilgrims were seeking political and religious freedom. Britain was not a pile of rubble as the result of war but a powerful kingdom when they set sail for the new world. Just my humble opinion.