Very quickly Billions of dollars would be redirected into the legitimate economy, and there would be far less need for American soldiers all over central and south America.
Until the early 1990s, the import of gold into India was restricted by the government and there was a large delta in the price of gold within India compared to the rest of the world. As a result smuggling of gold was very profitable and most of the Bombay underworld dons were gold smugglers.
One fine day the government lifted this restriction bringing the price delta to near zero and rendering the smuggling of gold, rather a waste of time. You'd think all the baddies would now be dis-empowered. No, they just switched to extortion and whatnot and are just as powerful and rich today as they were before - just doing different things.
It's like the Willie Sutton story. Q: Why do you rob banks? A: Because that's where the money is.
These drug lords are not in the drug business because they have a particular fondness for the trade but because that's where presumably the easiest money is. If that avenue is gone, they'll try and do other things - extortion, smuggling, counterfeiting etc.
Though I do agree with you that it would dis-empower some of the drug lords of South America, I disagree that it would have as great an impact on the economy.
As for the economic impact, I guess it would depend, but I'm inclined to think there would be lots of government revenues in it, if tobacco is any indication.