Purpose: Protect the cigar during handling, shipping, storing, and from mold, Lasioderma serricorne, etc.
Breathe: If untreated (and I suspect all cigar manufacturers use untreated cellulose hydrate) it is air-permeable and biodegradable. So yes, cigars can "breathe" (if by 'breathe' you mean can humidity transfer take place).
Aging: Again, yes. It'll happen slower, but it will happen nonetheless.
My experience: For several years, I unwrapped all cigars before they went into my humidors. Then, in response to some articles I read, I began to leave them in their wrappers to see I could actually taste the assertion that "uncelloed cigars aged together will mute each other's flavor profiles." Sounds logical, but after a year and half of unscientific testing, I have to say I can't really tell the difference. So I've come to the conclusion that I won't worry about it. If I get celloed cigars, they go into my humidor as such; ditto for the uncelloed sticks.
Google the question and you'll find some really good articles on the subject. Also remember, cigar makers know more than you do, and have done (and risked) a lot in deciding how to package cigars, so if it works for them, it works for me.
Happy herfing!