My impression was then when America tried to force other countries to participate in the embargo they told them to shove it.
https://en.wikipedia.org/wiki/Helms%E2%80%93Burton_Act
Also yes Cuba has trade with the rest of the world
http://atlas.media.mit.edu/en/profile/country/cub/
> Cuba is the 140th largest export economy in the world. In 2014, Cuba exported $1.74B and imported $5.91B, resulting in a negative trade balance of $4.17B.
> The top exports of Cuba are Raw Sugar ($392M), Refined Petroleum ($314M), Rolled Tobacco ($236M), Hard Liquor ($116M) and Raw Nickel ($108M), using the 1992 revision of the HS (Harmonized System) classification. Its top imports are Wheat ($234M), Refined Petroleum ($228M), Concentrated Milk ($207M), Corn ($204M) and Poultry Meat ($196M).
> The top export destinations of Cuba are China ($311M), the Netherlands ($157M), Spain ($141M), Senegal ($92M) and the United Kingdom ($67.3M). The top import origins are China ($1.05B), Spain ($920M), Brazil ($507M), Canada ($389M) and Mexico ($360M).
Of course geography still matters, the US is nearby, large, and rich. Exporting to the US would be a huge plus for the Cuban economy but it wouldn't change everything.