No, programming style can be "hacky", "script kiddie" or "architect kind design" or whatever. I'm speaking about "programming paradigms".
"functional programming, but that doesn't change the fact that SQL is a declarative language for describing recordsets"
ok, im describing recordsets for you: this set has 4223 records. I'm thinking of something else, but i can't really describe a recordset with anything else. Describing is not what you do when you create a software. You have a problem and you literally write a solution like an author write a book. And as you said, with SQL, you use a functional approach, how you do it when you use lambda or LINQ. Therefore SQL is functional.
SQL is turing complete with the structured extensions, so in that way can be general purpose, but something is general purpose or not does not decide the paradigm. Usually languages are more restrictive moving to the declarative side of things, but that is by design. The point is that you write less text.