As far as I understand it, an ozonator is only effective when the water is flowing.  So a circulation pump is necessary for optimal performance of the Ozonator.  
I have a 40-watt equivalent circ pump in my Hotspring  Jetsetter.  My insulation keeps the tub so quiet I can't even tell it's on if it were not for the large glowing logo.  Note - my tub is also located less than 3 feet from my bedroom wall so sound levels were a major concern to me.  Fortunately the circ pump is very quiet. 
Note the disadvantage is that this means your ozonator is running 24/7 which depending on it's hour rating, works out to around 2 years of use before needing replacement. The Circ pump is also another item to fail in the tub eventually.     Personally I feel the benefits of an ozonator outweigh the negatives, but that's my opinion.