Technically yes, but definitely not in the sense you think it's possible. It's not like abilities where you can simply inherit it from the parents. Unfortunately Hidden Power comes in tandem with IVs, which are an entirely different mechanic that are annoyingly difficult to breed.
Hidden Power is a much more complex and confusing mechanic than you think it is, so much so that it has its own annoying equation just to allow the game to figure out which type your Pokemon gets. This equation is driven mostly by IVs; this is where "Hidden Power breeding" comes into play. If you don't know what IVs are, they're not hard to understand. Each stat (Attack, Defence, etc.) has an IV value from 0 to 31. For level 100 Pokemon, one IV point is equivalent to one stat point, making them important for having Pokemon with good stats. However, the specific numbers from each stat's IVs also determines which Hidden Power type the Pokemon gets.
Since you do have some degree of control over which IVs get passed down in breeding, thanks to certain items like the Destiny Knot and the Power items, it is possible to pass down exact IV values from parents, which can influence your Pokemon's Hidden Power type. However, despite having access to these items, a lot of IV passing is left down to luck, and it can become a very tedious process. The process also requires you to know the parent's IVs exactly so you know which IVs you need to pass down, which is also very difficult to figure out.
So yes, they do work (in a way), but it's extremely hard to get right, and unless you're really dedicated, it's probably not worth your time.