They're definitely real, as long as you're buying a product from a country that requires accurate labeling. Afaik, there's no common fake HPA toothpastes you can buy at a store, even via amazon. Could be, but I haven't run across it.
Effective? It seems to be. However, not all dental groups have given it support yet. That doesn't mean it isn't effective, it just means they don't consider it a done deal, or haven't gotten around to it yet.
Of equal import, it doesn't seem to be more effective than sodium fluoride, and doesn't have some of the extra benefit of stannous fluoride. Plus, it's topical only. It won't hurt you if swallowed, it just doesn't do anything. Fluoride can be taken up via the digestive tract, HAP just breaks down in the stomach.
My take, after talking to my dentist and reading up, is that it isn't worth paying extra for unless you have some specific reason you can't use fluoride. If you can get it at the same price as your current toothpaste, fine. If you can't, then it likely isn't going to give you enough benefit to merit the extra at all