Yes, Fortune does work on Nether quartz ore. When mining Nether quartz ore with a tool enchanted with Fortune, there is a chance to receive a higher number of drops. The Fortune III enchantment gives a chance to multiply the drops by 2, 3, or 4. However, it is important to note that Fortune does not work on the quartz block, as it is a one-time item drop and cannot be legitimately reformed into its constituent block.