That's quite the unit, but I don't think a hot tub was what they had in mind for "Toys". I have seen it done though, twice. Both times were inflatables and one was carried in an HR side load TH, the other was ground-set after arrival. A 250-300 gallon hot tub more than likely wouldn't give you any issues weight wise when you were parked. I'm assuming that NOBODY in their right mind would attempt to travel with a hot tub filled in the back of their rig, although I would gladly pay a small admition fee to watch the first mile or two of the trip from a safe distance. Since there are pumps/heaters etc. that are designed for the smaller hot tubs I also doubt that you'd have power issues as long as you didn't attempt to run it through the RV itself and then fire up both AC's and the microwave.
Would "I" try this?? Nope, ain't my thing but as long as you're not thinking about installing a residential 8 person hot tub in the garage and driving down the road with the cover on to hold the water in I really don't see why not.
I would ask only one thing, once you get it set up please let us know where you're camped at, we would be happy to bring our own towels and adult beverages.