Leopard, I'm not an expert on the specifics, but corals do purify the water some by consuming some minerals. Xenia in particular is sometimes used in a refugium for nutrient export. However, unless you are adding a xenia refugium, I think it would be a bad idea to have the mindset that adding more corals is going to help keep the tank cleaner. The amount of purifying they will do is pretty small. So, for example, if you have excess nutrients such as nitrates or phosphates, adding more corals to the tank would NOT solve the problem but just mean you'd have more corals in the tank that aren't happy.
Adam, as for the time line for adding corals, I agree that it depends on the type. I added my first mushroom corals in about 3 months. I didn't add any LPS until about 6 months, and at about 8 months I added a few SPS (montipora) and an anenome. However, I wouldn't rely on time as the determining factor to when you can add things. It really has much more to do with how stable your tank is. In my case I had been extremely fortunate to have an incredibly stable tank from pretty early on. HTH
Kris