Independence from the English, yes, for the English chose to dominate Quebec in its infancy as conquered territory instead of as a partner. The United States would have welcomed Quebec as a partner and Quebec would be utilized much better and would have been happier. In fact, the Quebec migration in the 19th century would not have been necessary at all and of course I would not be here. As a product of Quebecois ancestors, I could easily see Quebec enjoying a golden economic age that would have make it lucrative for the people and for the United States. A Canada dominated by the English and their past grudges from far away cost Quebec many years of development.
Believe me, I think it would be great, because at least the United States appreciates the Cajun culture of New Orleans (who were there, by the way, because of the evil Deportation) and as tjadams said, survived just fine. The ONLY reason why Quebec is as it is today is because the upper classes of British subjects in Canada didn't give Quebecois a fair shake from the beginning, and the old French-English wars lived on. This would not exist with Quebec as a US state.