Just finished reading The Sugar Barons by Matthew Parker and the answer seems to generally be no.

North America had a self sustaining economy and population. People moved to colonies in America, put down roots, established families and ties to the land that eventually became more important. While the West Indian population was essentially transitory.

The region had so much disease and death that almost everyone who went there did so to get rich quick and then go back to England. West Indians tended to consider themselves British, while Americans increasingly became American.

The West Indies, had a tiny population compared to the Americas, but it made far, far more money. While they didn't have official representation in parliament, rich planters who returned home became politicians, creating a sugar lobby that had much, much more influence than the American colonies did, which they came to resent. The American colonies were also pretty deeply involved in smuggling, which frustrated and angered the British and West Indians.

However, the West Indians were extremely worried by the Revolution, they got most of their food from the American colonies, so there was some sympathy for them, they interacted all the time.

The sugar lobby pushed for a peaceful solution during the war, and a swift return the the status quo after the war.

I'd recommend you pick up The Sugar Barons if you're interested, or read the last few chapters on Google Books.