Yes, 'managed to do something' means 'succeeded in doing somthing, especially something difficult'. If you say "I managed to write a blog yesterday", you mean you succeeded in writing a blog or were able to write a blog yesterday.
You can't say "I could write a blog yesterday", though, because 'could' is not used to talk about particular ability in the past (on one occasion).
You can say, however, "I could eat a whole cake when I was little" - 'could' can be used for general ability in the past