Jim they use it around hot tubs all the time, but not where it will get wet. I think it will absorb water and become water logged over time if it was in direct contact with continuous water. I know they use it in exterior walk in coolers and freezers, if the roof leaks it will get water logged and loose it's insulation factor. A good test might to be buy a spray can of it and test it out.
If you are covered then the only water would come out of the hot tub getting in and out probably would not be that much. You might be better off to add a layer of Styrofoam sheeting directly under the hot tub so that water will run out the end and then spray foam under the sheeting, as you spray the rest of the deck.