It doesn't sound natural and I'm really not convinced that many people would get your intended meaning from it. 'A literary person/man/woman' is better. To express the idea that they have read a lot, you could use well-read, erudite, learned, an intellectual. These words do not express the idea that the person writes well though. You could say they are a gifted or skilled writer. You could say their writing is insightful, articulate, eloquent (depending on the aspect of their writing you want to praise).

You could say that and be understood, but it would be better to say, "He or she is well-read" In the US, his would be the most common way to say what you're trying to say.

I agree with Scott, or 'they are a very literary person'.