Not automatically—but it does make survival much harder for most plants. An urban planter box with no drainage holes has no reliable way to release excess water. After rain or a heavy watering, water collects at the bottom, saturates the soil, and pushes air out of the root zone. Roots need oxygen as much as water, so when the soil stays waterlogged, plants can yellow, wilt, stall, and eventually develop root rot. The plant is not killed by the absence of holes alone; it is killed by the conditions those holes normally prevent.
The risk depends on several things: plant type, soil mix, planter material, weather, and how you water. A moisture-loving plant in a cool, rainy climate may suffer slowly. A drought-tolerant plant in a sealed box can decline fast. If the box is outdoors and exposed to rain, the problem is especially serious because you cannot control how much water enters. Indoors, you have more control, but overwatering is still easy, and salts from fertilizer can accumulate because they have no exit route. This is one of the most common container gardening mistakes.
If you can modify the box, drill drainage holes. Several holes across the bottom—about 1/2 inch or 1 cm wide—usually make a big difference, especially with feet to keep the base from sealing against a patio. Do not rely on a “drainage layer” of gravel in a closed container; in a box with no holes, it does not create drainage and may actually raise the water table closer to the roots.
If drilling is not possible, treat the planter as a decorative sleeve. Put your plants in a nursery pot with drainage holes and lift it slightly inside the box so excess water can be emptied. Water sparingly, check the soil with your finger or a moisture meter before watering, and never let the box sit in standing water. A wick can help move some moisture out, but it is not a substitute for real drainage. You can also choose plants that tolerate moist soil, but even they will struggle in permanently soggy conditions.
Watch for warning signs: yellowing lower leaves, wilting even though the soil is wet, a sour or swampy smell, fungus gnats, mold, algae, or soft, brown roots. If you see these, stop watering, improve airflow, and consider repotting into fresh, well-draining mix. In short, your urban planter box may not kill your plants immediately, but no drainage holes are a serious risk. Drill if you can, use a liner if you cannot, and water with extra care. Your plants can survive, but they will do much better with a way for excess water to escape.