I'm in the San Francisco Bay Area and have never experienced a Band-Aid taste, though I'm not sure what a Band-Aid tastes like! But taste can be subtle, and I'm always looking to improve the beer, and this seems like a simple thing to do. If what day_trippr says is true and the band-aid taste forms during fermentation, then I could add it before pitching. Maybe I'll experiment with both ways.
I'm pretty sure that every municipal water system in the U.S. treats the water either with chlorine or chloramine, which is why we don't experience "Montezuma's revenge." Besides e coli, giardia is pretty much pandemic in wildlife and no reservoir or run-off water is safe. When I was a kid, I could go hiking in the Sierra Nevada and drink straight from running streams--no more! I've owned a cabin in the Sierra for decades and it used to be the water from the spring that feeds our small water system was safe to drink without treating--no more!
Chloramine may be used instead of chlorine now because, as someone said, it doesn't degrade and thus is more convenient for the water utility, but it's also better for the consumer because, unlike chlorine, it has no taste. When my utility switched it was a noticeable improvement--taking a shower was no longer evocative of a swimming pool, and the chlorine taste was gone. At the time, they did warn that aquarium water, for example, needed different treatment to make it safe for the fish. In times of drought in the Bay Area when the reservoirs get low, the water utilities sometimes draw supplemental water from the Sacramento river, and perhaps they increase the chloramine then, but it's always present in some amount.