I am going to ignore the issue of what is actually required or permitted by code, and make the point that a grounding electrode is IMHO a good idea for safety.
Regardless of any grounding electrode, the feeder/branch circuit going to this appliance/structure will include at least one grounded conductor electrically connected to a grounding electrode.
The hot tub almost certainly will include fittings exposed to the water, quite probably in contact with the water, and bonded to the electrical system ground.
The soil or concrete around this hot tub will almost certainly be wet when the tub is being used.
You have now set up a situation where the tub of water is at the ground potential of the house, by virtue of the equipment grounding conductor, the house grounding electrodes, and the bonding at the tub, while the soil or concrete around the tub is at the local ground potential, with both items wet, and people with very little clothing likely to be in contact with both. IMHO this is a perfect setup for electric shock caused by any sort of earth current (nearby lightning strike, stray voltage caused by improper neutral connection on a neighbor's property, POCO 'single wire earth return' wiring, etc.)
If this were my own property, I would want the UFER or a ground ring, regardless of what the code requires.
Note that this sort of bonding is required for an in-ground pool, including an 'equipotential plane' surrounding the pool.
-Jon