The natrual diet of a guinea pig is pretty much all grass so hay is not completely needed if they can graze on grass 24/7 but it's nearly impossible to let them do that and grass spoils when you try to cut it and keep it without drying. That's why we feed it as hay. Grass contains vitamins and minerals that are lost when the hay is dried but grass also has a higher moisture content. They need to eat more grass to recieve the same amount of nutrients as hay. If you think they eat alot now just try feeding them on a grass based diet. My 9 currently eat 1-2lbs per day of grass. If you are feeding more than just a little grass you should introduce it very very slowly or their digestive tract could get upset and try to ID the type of grass you have.
http://s142412519.onlinehome.us/uw/pdfs/A3637.PDF
Some types of grass actually aren't good in large quantities but these types are very rarely if ever used for hay such as fescue. Of the ones on that site orchardgrass, brome, bluegrass, timothy, and ryegrass are desireable. The rest like foxtail are ok but I probably would not feed them too much of it and fescue is best avoided unless you know it came from endophyte free seeds and that all your neighbors land is the same.