1. '0' readings just tell you that the level is 'undetectable' by that particular test kit and the level is quite likely not really '0'.
2. Our hobby grade test kits only test for inorganic phosphate, not organic. So, the level of actual phosphate in the system is higher (an ICP test will show both).
3. In nature on a healthy pristine reef, both phosphate and nitrate are very low (what we would see as '0' or 'near '0') on a hobby grade test kit), but food availability is much higher than we typically provide in a reef tank. The Zeovit system tries to emulate that very pristine low nutrient water quality, but has to some how make sure that the coral are getting enough nutrition in order to stay colorful and healthy. The system relies largely on providing bacteria to keep nutrients very low as well as providing coral nutrition (bacteria are one of the photosynthetic coral's natural foods along with by products derived from it's zooxanthellae's photosynthesis and zooplankton and/or phytoplankton).
To answer your specific question, corals can actually die if NO3 and PO4 levels are kept extremely low for a longer period of time without supplemental feeding. Corals have 'fat reserves' like other animals in the form of lipids, but once the reserves are gone they will be in dire straights if they can't replenish their energy reserves (by products from photosynthesis alone are not enough).
Many reefers report that keeping 'undectable' levels have allowed dinoflagellates to bloom since they typically out compete other organisms in very low nutrient conditions. However, having low NO3 and PO4 levels doesn't guarantee that you'll have dino blooms, just can make it more likely (especially if the system doesn't receive regular feedings which allow competing/predatory organisms such as microalgae, amphipods, worms, etc., to flourish).