What differences, if any, would this assay show if performed using raw (unpasteurized) milk?

The difference that would show if performed in unpasteurized milk will show that the raw milk will have more bacteria, and less oxygen then more of reduced dye methylene blue which is colorless.

In raw milk, the color will disappear quickly. Pasteurization affects the number of bacteria present in milk when pasteurization decreases the amount bacteria present in milk this is because of the heat shock of pasteurization bacterium enzymes are denatured. When the temperature rises the fluid which is inside the cell expands, and it increases the internal pressure and then it leads to cell burst.