It can be done, but I find that the water quality has always been better when I have skimmed. Water changes will only take a certain percentage of the dissolved organics out at a time, while the skimmer extracts them very efficiently. Plus a skimmer performs intense aeration of the water.
If you are trying to save money, I think it's false economy to not spend $100 on a skimmer when you will be spending a lot more than that on corals. If you want to try something more "natural," or are trying to raise corals that are more dependent on dissolved organics, then by all means give it a go.