No, the whole point was to CONTROL the production of those commodities for their own internal market. European economic thought during this time period was not based on free trade. It was extremely mercantalist which meant they wanted to keep as much specie within their own controlled customs territory. Controlling their own sources of these cash crops are important so that specie would not leave the country.
Buying sugar, cotton, and coffee would be preferable to not have them at all, but the European countries would all prefer to own the means of production themselves. This is why they all fought over islands in the Caribbean so that each country could produce the cash crops themselves and not rely on another power.