How can I protect a Nikon 200-500mm f/5.6 in rain across its full zoom range?

Yes. What you want is a rain cover/rainsleeve rather than a rigid shell. Flexible covers are designed to handle zoom lenses that extend and retract, acting like a bellows as the lens changes length.

Community members mentioned OP/TECH rainsleeves and more durable dedicated rain covers such as Think Tank models. A typical rainsleeve tightens around the lens hood at the front and wraps around the camera at the back, so the lens can still zoom while remaining covered.

If you only need occasional protection, disposable or reusable rainsleeves are a simple, inexpensive option. If you shoot regularly in bad weather, a purpose-built rain cover is the better choice.

One caution raised was condensation with simple plastic coverings, so in prolonged wet conditions a higher-quality breathable-style camera rain cover may be preferable.