Some of those little dots on VaultJumper's map may look unimpressive. Still, if the islands become part of the United States, everything changes in American history.
With the suggested arrangement, the United States becomes more involved with slavery. Britain loses some very profitable colonies, especially in the Caribbean.
Maybe Alexander Hamilton becomes President of the United States.
Napoleon may view the Americans as a threat. In which case, he may never sell Louisiana to the USA. Or he may embrace the Yanks as friends. Maybe he'll sell Haiti to the Americans. If the Americans are already in the area and they're defending sugar plantations and slavery, why not sell them Haiti and a few other islands? (What's the alternative?)
The United States Navy and the Marines become very important, at an early date. While looking to the West for national expansion, the Americans will also look to the Caribbean and even to Latin American.
Texas will attract a lot of American settlers, regardless of what happens in New Orleans.
Canada? Lots of Yanks will move into Ontario, and they'll continue to move to the West, all the way to the Pacific. There won't be much resistance (aside from some natives who won't have British support.)
By 1850, the United States will probably control all of the land that we identify with Canada. It's possible that the Americans will control Alaska. They will probably control Washington and Oregon.
Big questions: Who controls California and the American Southwest? What happens, if the Louisiana Purchase doesn't develop?