Yes, sharpeners work, in the sense that they put a somewhat useful edge on the knife at the cost of removing too much metal. It is a brute force method that drastically reduces the life of the knife. They will remove a ton of material and very unevenly. They should NEVER be used and they will damage the blades.
It's safer to sharpen your knives at home using widely available diamond abrasive household sharpeners that are safe for quality blades, unless the professional knife sharpening service uses a sharpener that doesn't overheat (detemper) knives or remove too much metal. Many professional knife sharpening services use traditional grinding stones, which remove too much metal and de-temper (overheat) the blade edge. Sharpeners that produce sparks are distempering the knife. The person doing the sharpening may not be properly trained.
The return of knives can take several days or weeks. Today, professional grade household knife sharpeners consistently produce a sharp edge every time they are used. Built-in precision angle guides take the guesswork out, and 100% diamond abrasives don't degrade exquisite blades. The edge formed with a traditional sharpening stone will not be as sharp or as strong as a cutting edge created by a professional household sharpener with built-in angle guides, unless the user is very competent.
The cutting edge of a knife must be precisely symmetrical to stay sharp longer. It will bend faster if it is tilted to one side. There are no angle signs on traditional stones to help create asymmetrical edges. They require time and effort, and they require a lot of time.
When sharpening a knife, the ideal is to remove as little steel as possible to obtain a very specific angle in the blade edge. The purpose of a sharpening is to keep a sharp knife sharp, and it is not intended to be used to sharpen a blunt knife.