Short answer: in most urban balcony setups, yes—or at least you should use some form of protective liner or tray between the planter box and the balcony floor. Urban planter boxes are exposed to rain, watering, condensation, fertilizer salts, and soil moisture. Even a planter that looks sealed can weep, stain concrete or tile, leave rust marks, or scratch the floor when it is moved. A liner is inexpensive insurance for tile, stone, concrete, and wood-composite balcony surfaces. However, the liner must manage water properly; it should not trap water inside the planter.
A liner helps protect the balcony floor from water stains, mineral deposits, fertilizer residue, rust, scratches, and root staining. It also makes the planter easier to move and clean. If your planter box has drainage holes, place a waterproof tray or saucer underneath it and use pot feet to keep the base above standing water. Do not seal the drainage holes. If the planter is made of wood or metal and you want to protect the floor from interior moisture or rust, line the inside with a waterproof membrane, but build a proper drainage layer with gravel, geotextile fabric, and overflow holes. Pond liner can work, but it must slope toward an outlet; otherwise, it becomes a bathtub and can cause root rot.
You may not need an interior liner if the planter is a self-watering box with a sealed reservoir, overflow holes, and adjustable feet, and it already sits in a drip tray. Even then, use a waterproof mat or tray if the balcony floor is sensitive. The best setup is simple: a waterproof tray or mat under the box, pot feet for airflow, working drainage holes, a geotextile layer, and regular cleaning of the tray. Check the weight and overflow risk, and never drill into the balcony floor. In short, yes—use a liner or tray if the planter sits directly on the balcony floor or has open drainage. Choose the right type: a tray under the box for floor protection, and an interior waterproof liner only when drainage and airflow are designed correctly.