CamLoch,
If you increase the flow on the water side, the heat transfer cofficient on that side will increase, of course, increasing the overall heat transfer coefficient. This will increase the delta T on the other side. However, I don't think it will increase the overall heat transfer coefficient enough to result in a higher delta T on the water side.
As IRStuff pointed out, the water side delta T is inversely proportional to the flow rate if the Q is constant. It's a pretty good bet that the effect of the water flow is greater than the effect of the increased heat load.
Speco