Yes, provided you compare like with like. Recirculating systems, on which aquaponics is based, operate with a daily water renewal of just a few per cent of the total volume, whereas open pond farming involves large-scale water replacement. French pilot projects put the saving at around 90% less water than conventional production.
On a domestic kitchen garden scale, the comparison also favours aquaponics over growing in open ground. Water is neither drained deep into the soil nor lost through run-off — it circulates in a closed loop and only leaves the system through evaporation, plant transpiration, and the small amount carried away with the sludge removed from the filter.
In practice, regular top-ups are still necessary, particularly in summer and in a greenhouse where evaporation increases significantly. Rainwater harvesting is preferable to tap water, whose chlorine must in any case be neutralised or allowed to off-gas before being added to the pond.