None of the following resources seem to think so: Merriam-Webster, The Free Dictionary, Oxford Dictionaries, Collins.
But Cambridge Dictionaries Online says it is informal.
And it appears on Urban Dictionary, which tends to signal something.
Learn English – Is the word ‘cocksure’ considered informal, non-PC, or even vulgar
formality
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Best Answer
It wasn't originally, because it's from cock meaning rooster --proud as a rooster. However, I'm sure many people these days --particularly those who are younger --would associate it with a vulgarity (due to the fact that the use of the root word to mean rooster has been eclipsed by its vulgar use).
Just one of any number of terms whose associations have coarsened over time.