After just 6 weeks I know I personally couldn't do it. I might last a day or two, but I know myself and temptation. Something would tell me it would be OK to have just a few. Most likely I would say, "I paid all of this money, I may as well use it."
If you want the Caribbean you can always take a cruise. Sure, there's plenty of alcohol, but at $10 a drink I know I'd be less tempted.