They do look rather weird, don't they? But I very much doubt, that the beak did anything to help stay healthy. Reports from that time specifically mention that those who help the sick are the first to become sick themselves. Also the way of infection is not the air you breath but normally the bite of an infected parasite (most commonly fleas) which are not really repelled by parfume worn in a beak.
However, this rather ghoulish attire is a first step away from praying and hoping for some angelic help towards finding a logical solution. Thus I find this dress extremely fascinating.
And let's face it, as we can't recognize anybody wearing this outfit it leaves room for all kinds of spooky ideas about the persons wearing them.