Does the ultrasonic pest control device protect the whole house if installed in for instance the kitchen?

When your pest problem is limited especially in a small house it could work out just fine to attack the symptom itself (pest entering the living spaces!) by means of one or several units of the junior Topo Stop model 'Electro Cat'.
For such a 'budget installation' you must be aware of its limitations since the ultrasonic sound waves won´t penetrate the wall paper! If the struggle for survival calls for it the rodents might be forced to make a sally from their hidden bases in the wall notwithstanding the presence of an ultrasonic pest repeller.
The mice Gus and Jack in Walt Disney´s Cinderella clearly illustrate this when they despite great anguish enter the room in order to try to pinch Cinderella´s necklace which is being guarded by the cat Lucifer.

The answer to the question is therefore: In principle NO! In order to optimize your pest control installation you should always try to put the device(s) in the primary entrance spaces of the vermin such as the attic and/or the crawling space underneath the ground floor.

N.B. Some electronic pest control companies claim that one single unit of theirs installed in a room will effectively clear the whole house from vermin. This is not true! Since ultrasonic sound waves by nature can´t penetrate walls or floors there is no way their device will affect any vermin outside the living space. You can ask any audio physicist about this!
Yet other companies respond to this scientific fact by claiming that the electromagnetic field generated by their device still makes it work throughout the whole house.
These so called 'electro puls' devices have not proven to have any penetrating effect and in 1980 the EPA and U.S. Postal Service took action to remove all "electromagnetic" (not ultrasonic) pest control devices from the market. Health Canada has banned the sale of electromagnetic pest repellers in Canada because there are serious questions as to the advisability of increasing one's exposure to electromagnetic energy.