I'm thinking it might be alright in my situation, since the only time it would really be touching chlorine is when the cover is rolled onto the reel, otherwise the grommets would be up out of the water. Hrm.
Back in the day, brass hardware was commonly used in pool equipment. Before the plastic butterflys, brass bolts and wing-nuts held your attachments to your pole. Brass ball floats held up the the rubber vac hoses that could not float on their own. Of course, with no CYA, FC was normally 1-3ppm. I think they will hold up just fine.
I probably should've qualified what I said. In pool concentrations, I think brass will function just fine. It'll corrode very, very quickly but it will not be unusable. If you don't mind the look, I would use it.
Brass is an alloy of copper and zinc. The rate of corrosion is higher when the percentage of zinc is higher. Keeping the zinc below 15% and adding a small amount (1%) of tin can make the brass more resistant to corrosion as described here.