As for me, even if they would have internet access or contact outside their country, it will still take time for them to access cryptocurrency. They will be needing time to study about its purpose and the function of it. It will still take a long process of learning. I wonder if they would have an interest in crypto market if their technology hasn't been well developed.
Cuba is a very interesting country and right now people have already access to the internet (started last December 2018) which can be opening doors for cryptocurrency market to slowly evolve. Right now, I think there is no official stance from the government whether they have the inclination to make cryptocurrency legal or banned (just like China). Will this mean that people will soon demand from the government to allow them to join the cryptocurrency movement? Most likely the government will not allow such a thing.
Here is an interesting read on the same topic:
https://bitcoinnews.com/internet-comes-to-cuba-will-cubans-comes-to-crypto/Cuba is a country ruled by leaders who do not believe so much on an open market and the government controlled almost all aspects of the people's lives. I think this is a situation that cryptocurrency will not grow and flourish though the potential is really there.
I'm trying to get in contact with @HAVBlockchain (founders of the Havana Blockchain Center)
https://www.bitcobie.com/entrevista-havana-blockchain-center/ and @BitcoinCuba on twitter right now see if they can provide more informations.
The article stating that they started having access to internet in December 2018 is false. They are able to have "in-house" internet as of 2017 if they can afford it "very expensive" and they were able to access internet wifi points since 2016 using Etecsa internet cards which sells for 1.5 CUC for 1h.
Most likely the government will not indeed. But as of now, from what I'm reading it is unregulated as they are ignoring it because it is too tiny.
I agree on your point about the government, I have many friends living there and have witnessed some of the most absurd situation.
I believe the first step toward any kind of cryptocurrency movement in Cuba would be education about the technology which would, in my opinion, be highly doable.