Well geez, leave the cheese off the burger
There's nothing wrong with adding underlayment over your subfloor to stiffin it up, if you feel that's necessary. Keep in mind, most manuf. require the substrate to be flat within 3/16" in 10'. So if any of the existing water damage has swelled areas in the pb, you will want to sand that flat first.
You shouldnt have to worry about moisture from underneath as long as the crawl space has adequate cross ventilation, no leaks, etc. I would consider laying out 6 mil plastic in the crawl space, if it's not there already.