Hi Bill
Yes, Paulownia will air dry in very short order. When we've sawn some logs we usually slab it to 8/4 and it will usually air dry to your particular area in 6 to 8 weeks, give or take a few days. Here, with the drought on about half a dozen years, the air is dry and we've had it dry to about 18% in a month. It will kiln dry to 6% in about a week or two after that.
I would venture to say you could probably find one of those dealers that would sell you a log, if you could transport it. You could make a lot of boats or a lot of money, cutting it down to 2x's and storing it. It holds up well, doesn't warp or crack if cut and prepped properly.