Not necessarily. For most urban planter boxes, you do not need a specialty drainage-hole kit or professional equipment. A basic electric drill or cordless drill and the correct drill bit will usually be enough. The key is matching the bit to the planter material, because the wrong bit can crack ceramic, wander on plastic, or burn through metal.
For plastic planters, a standard twist bit works well. Mark the hole positions first, use a low speed, and support the base so it does not flex. A 1/4- to 1/2-inch bit is usually sufficient, and several smaller holes often drain better than one large hole. If you are working with thin plastic, a step drill bit or a sharp awl can also help, but a normal drill bit is still the simplest choice.
Wood planter boxes are easy to drill with a wood bit or a general-purpose twist bit. Concrete, brick, or stone planters are different: you will need a masonry bit, and a hammer drill can make the job much faster. Ceramic or glazed planters need a tile or glass-and-tile bit, plus light pressure and water for cooling. Metal planters require a metal-cutting bit and a little cutting oil. These are not special tools in the sense of rare or expensive, but they are the right bits for the material.
Before drilling, measure and mark the holes, wear safety glasses, and place a scrap board behind the exit point to reduce chipping. Drill slowly, especially with brittle materials, and keep the hole slightly raised from the ground so water can escape. If the planter will sit on a balcony or patio, use a saucer or tray to catch runoff and protect the surface.
So the honest answer is that you need the right drill bit more than a special tool. If you only have one plastic or wooden planter, a basic drill and a standard bit may be all you need. For concrete, ceramic, or metal, buy or borrow the correct bit before you start. That small step is what prevents cracks, damaged bits, and a planter that still holds water after all your work.