Let's not beat around the bush Fallon was playing off the stereotype that black men with dreads coming from the Caribbean are drug smugglers. It's a common stereotype, you might not find it funny but that's what it is.
I remember watching Fallon when he first got his late night show after Conan went to 11:30. It was an absolute train wreck. He had no stage presence. He was nervous with no charisma. Absolute embarrassment. But I love The Roots so I would watch it from time to time and he got really good. It was cool to see someone start something unfamiliar and get really good at it over time. His comedy isn't for everyone but his target audience loves him.
Has more to do with the huge smile and half open eyes than race. No doubt the dreads helped too, but do you think he wouldn't have made the same joke if he were white?
Everyone is a trainwreck when they first start, that's the nature of the business, but he's really hit his stride and his taped bits are up there with the best that Conan has ever done (his only competition for taped bits), plus his show just exudes an aura of fun that you can feel coming off of the guests.