Short answer: yes, it can—and if your balcony gets direct sun for most of the day, I’d assume it will fade at least a little. How much depends on the material, the quality of the finish, and how much UV it takes.
Cheap plastic or resin furniture is the most likely to fade. Whites turn yellow, bright colors go chalky, and dark colors can look washed out. Better resin or HDPE pieces are usually treated with UV stabilizers, so they hold up longer, but they’re not completely immune. Metal frames are different: aluminum itself doesn’t really fade, but the powder coating can chalk or lose color. Painted steel can fade and peel, and if the paint fails, rust may follow. Wood is a mixed bag. Teak and eucalyptus often weather to a silvery gray, which some people like, but if you want the original honey tone, you’ll need to clean and oil it. Painted wood will usually fade or peel in strong sun. Fabric is often the biggest problem. Cushions, slings, and parasols made from standard polyester or cotton blends can fade quickly. Solution-dyed acrylic, like Sunbrella-type fabrics, is much more UV-resistant. Synthetic wicker can fade too, especially dark brown or black resin strands, though higher-end versions do better.
Urban balconies can be tougher than a backyard. Glass windows and metal railings bounce light and heat onto the furniture, concrete floors radiate warmth, and there may be little shade or airflow. Even if it doesn’t rain much, UV alone can break down dyes and finishes. Pollution and dust can also make the surface look duller.
What can you do? If you can, add shade with an awning, umbrella, or pergola. Rotate the furniture or move it out of the worst afternoon sun. Use breathable furniture covers when you’re not using it, and bring cushions inside when you can. Wash off dust and bird mess regularly, because grime can hold heat and moisture. You can also use a UV protectant made for outdoor plastic, resin, or fabric, but test a small spot first. And when you buy new furniture, look for UV-stabilized resin, powder-coated aluminum, teak, or solution-dyed acrylic.
So will it fade? Probably, at least somewhat, if it sits in full sun all summer. Budget pieces and fabric cushions are most at risk. Good-quality outdoor furniture can still change over time, but it usually fades more slowly and stays usable. If you love the color, cover it or move it; if you’re okay with a little weathering, it may be no big deal.