The answer to this will depend to a great extent on the size of the country and the degree to which the trafficking dominates its economy. Let us look at two examples.
In Mexico, there is a great deal of drug trafficking but also a relatively large economy with many other important sectors. Because of this, the economic impact of the drug smuggling per se is limited. There is an economic impact from the violence that currently surrounds the trafficking, but that is a different issue.
By contrast, we can look at a country like Tajikistan. As seen here, drug smuggling completely dominates the country's economy because it has very little else in the way of important economic activity. When drug trafficking dominates an economy this way, the effect is similar to what happens when a country becomes oil-rich. The one industry becomes so dominant and such an easy source of money for those who are in it that there is little incentive for them to try to diversify their economy. The people who have the money do not need to or want to invest it in other economic sectors. In this way, drug trafficking can stifle the economy of a small country.