Does Galvanized Steel Rust?
Technically yes, however, hot-dipped galvanized steel resists corrosion in numerous environments for much longer than uncoated steel.
Whether it is paint or galvanised steel, any coating is designed to protect the base material. The coating corrodes instead of the core material. Any moisture and corrosive materials (including oxygen in the air) will eat away the coating first before oxidising the metal underneath.
When you have a galvanised coating the zinc will oxodise instead of the metal it is coating. Zinc oxidises slower than uncoated steel, preserving your sheds structural integrity.