The short answer is: it can rust, but it will not necessarily rust just because it gets rained on. Rain is only one part of the equation. Rust needs iron or steel, oxygen, and moisture. An urban planter box left outside in rain will be at risk if it is made from untreated or poorly protected mild steel, iron, or thin metal with scratches and exposed edges. If water collects in the soil, at the bottom of the box, around fasteners, or under a saucer, the metal may stay damp for long periods. That constant moisture is usually more damaging than a passing shower.
Material matters most. Powder-coated steel can last for years outdoors, but once the coating is chipped or scratched, rust can start at the damaged spot and spread under the paint. Galvanized steel has a zinc coating that slows rust, though it is not permanent, especially in coastal air or with fertilizer salts. Stainless steel and aluminum are much more resistant to rust, although aluminum can oxidize and stain, and stainless steel can corrode in salty or chemical-heavy conditions. Corten or weathering steel is designed to rust on purpose; it forms a protective patina, but it can stain patios and walls, so it needs careful placement. Wood, plastic, composite, and concrete planters do not rust, though their joints and fasteners might.
Drainage is critical. A planter box without drainage holes, or with holes blocked by soil and roots, can become a wet container. The bottom sits in water, and metal stays wet even when the surface looks dry. Raise the box slightly off the ground with feet or spacers, keep drainage holes clear, and avoid letting the planter sit in a puddle. A liner can separate soil from metal, but it must still allow water to drain. If the planter is already painted or powder-coated, inspect it each season and touch up chips with a suitable metal paint. Use stainless or galvanized fasteners where possible, and keep fertilizer and salt-heavy products away from bare metal.
So, will an urban planter box rust if you leave it outside in the rain? It depends on what it is made of and how well it is protected. An untreated steel or iron box with poor drainage is very likely to rust over time. A well-coated, well-drained, rust-resistant planter can stay outside in the rain for years with only routine care. If you want low maintenance, choose stainless steel, aluminum, plastic, composite, or a sealed and powder-coated metal design, and check drainage before you fill it with soil.