My experience with kleenex and paper towels that make their way into manure piles is that they do not break down as fast as you might expect but they do break down. Personally I would not hesitate to compost them, if I were organized enough to separate them out
It had occurred to me, your fellow allergy sufferer, to do the same thing. But theres nothing I hate worse than wet toilet paper-y stuff and I couldn't imagine being faced with that every time I turned my compost.