In fact the pH of both distilled and DI water can be measured, and in the case of freshly prepared water both should be in the vicinity of 7 pH, though the measurement sensitivity/accuracy will be somewhat dependent on the residual ion content and the condition of the pH meter. As both waters are exposed to the atmosphere, they will absorb carbon dioxide which gradually reduces the pH to a typical pH range of ~5+ to 6.5.
You might want to consider conductivity as a more reliable measure of distilled/DI water purity.
You have to use a specially designed electrode to do it. It has to feed a KCl solution inorder to have enough conductivity for the electrode to function. Highly demineralized water is a very good resistor to current flow until contaminated with atmospheric gases, etc.
I actually prefer to use resistivity rather than conductivity for highly demineralized water. Most people do not comprehend that a conductivity change from 0.055 uS/cm to 0.1 uS/cm is just as significant as a resistivity change from 18.2 M Ohm/cm to 10 M Ohm/cm.
Since water dissociates to produce one hydroxyl ion for each hydrogen ion, it is possible to measure the pH of distilled water or deionized water. However, the pH of distilled or deionized water has little significance as a reference point in water chemisty and therefore is of little importance engineering practice.
