Yes, the Health Care system in Cuba works.If you judge efficiency by waiting times and getting treated, yes it is efficient. There is no private sector medical system.Visitors to Cuba normally purchase private health insurance in their country of origin prior to visiting Cuba as holding medical insurance is a condition of entry into the country.
Cuba probably has the highest ratio of Doctors of any country in the world and uses it's medical graduates very effectively by supplying medical teams to other countries. The best known example being the exchange of medical services for cheap oil from Venezuela. However, having provided free education for Doctors, it is very difficult for Cuban doctors even if they have obtained a passport, to leave the country individually as they require the carta blanca and the government usually will not issue them one, thinking that if they leave they won't return.
I have used Cuban medical services and the treatments received have been excellent and prompt.
