We can look at another Catholic power involved in the Americas for some illumination. Spain didn't see the protestant issue, they saved all their persecution for Jews. What we have found is that many Jews were involved with the Americas (some even think Columbus was Jewish). They still stayed "crypto Jews" but didn't suffer the indignities that they would have in Spain, where you could be pantsed in public if you were suspected of being Jewish to see if you were circumcised. They maintained deep cover in the New world regardless, but they have found Jewish cemeteries in the San Luis Valley and through New Mexico and the southwest, the key point being that it wasn't until the 60s or so that this was discovered. So maybe the Huguenots could emigrate, but the political deal between the monarchy and church would probably keep them oppressed in the Americas, as it did for Jews in Spanish America.

The dissenters that left for America were in trouble for their proximity to people who would have bad outcomes if the dissenters prevailed, so moving to America relieved the political pressure. The dissenters also tended to be fans of living experiments, Quakers and puritans wanted a new society, but believed pretty much the same things as Anglicans, a geographic solution would work in this case.