Taking a sample of the distilled water to be measured would be frustrating. The pH of ultra-pure water is difficult to measure. Not only does high-purity water rapidly pick up contaminants - such as carbon dioxide (CO2) - that affect its pH, but it also has a low conductivity that can affect the accuracy of pH meters. ( Source:Why doesn‘t my pH Sensor read pH 7 in distilled or deionized water? - Vernier Tech Info Library #1286 )

Only recently produced unexposed distilled water has a pH-value of approximately 7. At that protected instant, distilled water is ideally nothing but hydrogen and oxygen molecules and no additional gases, minerals or contaminants.

The pH of pure distilled water is easily altered by contaminants. Once a contaminant is added, the water is no longer pure and the pH will change depending upon the contaminant. Oxygen and nitrogen both dissolve in water but have little affect on pH. CO2 gas in air has a high solubility.

Distilled water readily dissolves carbon dioxide from the air. Carbon dioxide from the air dissolves in distilled water(and RO water) until the water is in dynamic equilibrium with the atmosphere. The total amount of the CO2 in the water is determined by the CO2 concentration in the atmosphere. Dissolved carbon dioxide reacts with the water and forms carbonic acid. Within a couple of hours, absorption of just a few ppm of CO2 will cause the pH of ultra-pure water to drop to 5.0-4.5.
Sources: Deionised - Demineralised Water - Lenntech and
The pH of Distilled Water