Well, it is soaked in the blotter but like a soaked sponge the outside will still have some on it, so yes you can rub some off I suppose. How much is soaked inside versus how much is on the surface though depends on how thick the blotter is.
As far as storing it goes, the most important thing is to keep it away from the sun. Tin foil is good for this. I'm not sure how big of a difference temperature makes though. Obviously avoid extreme heat and such but I've heard of blotter from the '60s being stored between pages of books at room temperature and still being just as potent now.