I'm going to be getting a couple of induction hobs, but I am wanting them mounted underneath a thin (approx 5mm) piece of wood. Is this possible from the safety point of view and would I have a major worry about efficiency?
Induction hobs work by creating a magnetic field which causes electrical currents in the base of the pot or pan. These currents heat the pan through normal electrical resistance. The further away the pot is from the hob, the weaker the magnetic field, so you're going to lose a lot of efficiency right there.
From a safety point of view, there are several oils that have smoke points over 400 °F so if you ever fry your food, you'll probably start to see the wood charring.
Finally, how are you going to keep the wood clean? Any spills are just going to soak right into it.
Heating a pot thru a sheet of paper works perfectly well as long as you stay below the paper's flash point. This is actually useful when making jam or similar sticky foods, or when you want to use a cast-iron pot but are afraid it will scratch the surface. The classic demo is boiling water, for the same reasons you can boil water in a paper cup.
But paper is cheap, disposable if it stains or scorches, , and burns out rapidly if it ever does ignite. A wood countertop would be a very different matter. Can't recommend it.
By the way, if you're interested in induction cooking, be aware that the pot must be of a magnetic metal. Aluminum pots will be unusable except in the oven, as will some (not all) stainless steel. Be sure to include that in the cost of switching over.
Further discussion of the practicalities of induction cooktops probably belongs on the cooking portion of SE....?