I went through a period when I was a foster mom and every kid I got seemed to come with pink eye. I used a herbal eyebright wash and it worked as fast as the prescription. I did get my kids doctor to write permission to use this instead of the prescription as he had little faith in those drops anyway.
However, I get the impression that some daycares are looking for a reason to send the kids home. If you tell them that you are treating the pinkeye, and will take care of it at home, you might get away with not telling them you are treating it without a doctor. I got away with this with my son and ear infections but we were seeing a chiropractor and I just kept saying my doctor was ok with our treatment which was true.
It kind of depends on how aggressive your daycare is about proof of medical treatment. Thats one thing I love about my new home care. She is much more open about herbal, natural treatments and I never have to hide the truth like I did in a center.