What if's are overall quite pointless, but consider how in very few cases emigration truly solved everything. Ireland was never pacified, the emigration of puritans did not stop them from being pivotal in the English Civil War, etc. So, most probably, it would have mattered little. Remember that the Huguenots in France were also often well-off groups with vested interests and not necessarily with much incentives to abandon all that.

Interestingly French short lived colony in Brazil in second half of 16th century was a haven for Huguenots

https://en.m.wikipedia.org/wiki/France_Antarctique

In the US the narrative of colonization for religious reasons gets over played b/c it's a nice story. But what really drives colonies are institutions, usually financial. England was set up to make more money off of colonies b/c it's institutions, like corporations, banks, credit systems, shipping, etc. were set up to exploit those opportunities. The French just weren't at the same scale.

Likely not. For several reasons.

One, a number of powerful nobles had embraced Calvinism. John Calvin himself believed that the reason the Huguenots were able to flourish was the conversions of nobles like Jeanne III of Navarre and Louis I, Prince of Condé.

Two, the French crown was in dire financial straits, which would have made it unlikely for them to support expeditions in the Americas (which often failed). The lack of funding itself was a major reason why the Wars of Religion kept reoccurring: the crown lacked the funds to either enforce the majority of its edicts of tolerance or destroy the Huguenots entirely. This was because the constant warfare Charles VIII, Louis XII, François I, and Henri II had waged against Italians and/or the Habsburgs had drained the treasury and the reoccurring civil wars disrupted agriculture, which just created something of a vicious cycle.

Third, religious tension in Great Britain wasn't actually eased all the much by having colonies. While some Puritans were fine going off to Massachusetts Bay Colony, there were plenty of them that weren't, like Oliver Cromwell, and that other issues led to the Wars of the Three Kingdoms.

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.