It is not just a case of protein percentages, but the right kinds of protein. Protein is made up of amino acids, which the food is broken down into by digestion. These amino acids (AA) are re-formed in different ratios into new protein that builds muscle for what the pig needs. There are 10 needed in food to allow the pig to grow (called essential amino acids as the pig can't make them). Pigs being omnivores need "meat Protein" as well as vegetable protein to get the right amino acids. Apart from worms, bugs etc. pig feed has these proteins in it, principally soya, and from AA's added such as lysine.
So yes hay will provide some nutrition, and KK's needing a lower protein level can cope with hay and haylage as HH states , but for most pigs it will provide great interest (which is why we feed it) but not to the extent that you can drop off pig feed.
So use as a supplement, not a replacement or cost saver - otherwise you'll find that your pigs grow slower so take longer to finish giving a false economy.