Not necessarily. One of our cats will disappear over the horizon if a high-pitched whine, such as from our vacuum cleaner, occurs. In fact, I only have to get the thing out and he's gone, knowing what's coming. Same with the robomower - sits there quite happily sunning himself but as soon as the mower gets going he is gone, and that's a very soothing kind of hum but high-pitched.
OTOH, our other cat couldn't give a toss. So maybe they work on some individuals and maybe they don't on others. Clearly, if the aim is total annihilation then they don't work (and much else wouldn't either), but if you just wanted to show they do work - as in having an effect - then you only need one or two critters to scuttle away.