A study in Japan looked at the difference in oxygen uptake between unaided arm-stroke-only swimming and paddle-aided arm-stroke-only swimming. The findings showed that although paddles obviously allowed faster swimming, this was entirely due to the higher propelling efficiency of the swimmers and not to any increased energy production.

Thus, if it is purely physical improvements one is looking for, the use of hand paddles offers no advantage. However, their usefulness in increasing one's 'feel' for the water undoubtedly exists, as I'm sure readers who are involved in swimming will agree. It is also true to say that the state of training influences swimming efficiency, and that well-trained swimmers have higher efficiencies than the untrained at any given swimming speed. (Ogita and Tabata, 'Effect of hand-paddle aids on oxygen uptake during arm-stroke-only swimming', European Journal of Applied Physiology, 1993, vol.66, pp489-493)