I have to assume that your temperatures are only a few degrees off and a small quantity of water is added. Since you are using RO water that has little alkalinity, its effect on pH should be minor. However, there could be a slight increase in the mash pH since you are diluting the acid content. The same thing occurs when mashing with a thick versus thin grist ratio.
Of course, you would be diluting the ionic content that you were targeting with the original mineral additions, but if the cool water addition is small in comparison to the total mashing water volume, then the effect will also be small.
It doesn't sound like this is a serious concern. I do agree with the others that recommend using ice cubes since there is greater temperature reduction per unit of added water.