Yes—most of our urban outdoor furniture comes with weather-resistant cushions, but it does depend on the specific piece. The cushions we use for patio sofas, sectionals, chairs, and benches are usually made with performance covers like solution-dyed acrylic or olefin. They're designed to resist fading from UV rays, handle light rain and humidity, and reduce the chance of mold and mildew. Inside, many use quick-dry foam so they don't stay soggy after a shower. The covers are often removable and machine washable, which makes city balcony life much easier.
A few frames are sold without cushions, and some budget sets may use standard cushions instead. So if weather resistance is a must for you, check the product details or filter for "weather-resistant cushions" before you buy. For the longest life, bring cushions inside during heavy storms, let them air dry completely, and clean them with mild soap and water. If you tell me which set you're looking at, I can confirm exactly what cushions it includes.