No. You do not need to be fit before starting CrossFit. Every workout scales to your current level, so the class builds your fitness rather than assuming it. Coaches adjust weights, movements, and pace on day one, which is exactly what beginners and returning exercisers need.
This is a direct answer from the CrossFit BC coaching team. Short version first, then the detail and the local context for training in Vancouver. If you want the same answer applied to your own situation, a coach will walk through it with you in person.