I also have a Jason air tub...mine came with a formed foam panel on the bottom designed to sit flat on the floor holding the tub nice and level (assuming the floor is).
You should be able to do what you are planning, but the box may not be necessary if you use deck mud. I'd also consider a sheet of plastic on the gypcrete. This will stop it from wicking moisture out of the mix which makes it weaker. Deck mud is 4-5:1 sand to portland cement mixed and wetted enough to hold into a ball when you grab and squeeze a bunch. It should not be wet enough to drip when you do this.
If yours has the same foam panel molded to the bottom, you could build a raised platform for it to sit on. The mortar would account for any inconsistencies in the floor, but I'd expect the gypcrete to be dead level, so a platform could work as well.