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No, I think creativity, originality and imagination are more important!
No it is not necessary. Writing is a gift or a talent; when somebody is gifted in writing nothing can stop him from doing so!
I agree with all answers given to some extent.
The key to answering the question is realizing the word "necessary" is present. What I mean is, if you are a writer, I will consider that you are talented/creative, that is a given, otherwise why would you be a writer?
So, back to your question, I would say yes, it is necessary to write correctly (grammatically) to be a good writer, otherwise your text would be unintelligible or at the very least not enjoyable.
To communicate an idea in writing, it has to make sense first and foremost. Nevertheless, one does not need to be good at grammar in the sense of knowing names of grammar points and all the rules, etc.
Bottom line is that grammar is a great tool for the connoisseur.
It is like having a building made out of improper material. The building might look good but it will not last long.
To be a good writer, one has to be talented to begin with, and any Grammar will add on later
It is often said that you have to know, and understand, the rules before you can break them. Great stream of consciousness writers like John Don Passos famously adapted his grammar - but he was always understandable. So did e.e.cummings ... who neglected capitalization. In arguably one of the great novels, James Joyce's Ulysses, the rules were often bent - in order to faithfully reflect the speech of those particular Dubliners. But, it is pointless to write in a way that few others can understand. And, there is a standard international English that all English speakers can comprehend.
No, being good at English grammar doesn't necessary mean being a good writer.
