It doesn't all transfer that easily
I read something today that made me realize that lots of folks think that if you're a good writer--if you have a strong knowledge of written English or proven success in some type of writing--then you'll make a strong legal writer.
Even a superb grounding in writing English does not mean you'll be a good legal writer. Or a good fiction writer, or a good poet, or a good news writer, or a good science writer, or anything. Legal writing, despite what many say, is different from other types of writing, just as fiction is different from news writing and poetry is different from science writing.
Yes, a solid grounding in writing is a huge head start to becoming a good legal writer. (Many law students lack it.) But you will still have much to learn about law and the conventions of legal English. Besides, legal writing comes in at least three varieties: objective analysis, persuasion, and drafting. It's complex and idiosyncratic.
Even if you do not have a good background in writing English, you can still become a good legal writer. But the gains will come from your own efforts, study, and practice. Your law-school legal-writing course can only teach you about law, legal English, and legal writing. It can't and won't give you a solid grounding in writing if you lack it.
If you do have a good background in writing, you still might not become a good legal writer. Your legal-writing course can't and won't give you the energy and drive to become a good legal writer if you lack the motivation.