Recent experimental studies have suggested that zeolites, if present on the Martian surface, could undergo a strong diurnal cycle of hydration and dehydration with possible impact on the atmosphere. This study evaluates this possibility using a global model of hydration/dehydration of two different zeolites (clinoptilolite and chabazite) assuming actual diurnal, seasonal, and geographical temperature variations. If zeolites extensively cover the surface and undergo complete diurnal hydration/dehydration cycles as predicted from the water vapor adsorption isotherms, the resulting water content would be too high in both the surface material and the atmosphere, implying that the abundance of zeolites is low or that zeolites must exist in a more desiccated state. If the zeolite abundance is low with the same hydration behavior, the lowest mean surface water content would occur at the equator, which also does not agree with observations. If substantial hydration/dehydration occurs seasonally rather than diurnally, the latitudinal and seasonal variation of the water content becomes too large and the zeolite abundance would have to vary with season to match the observation, which is also unrealistic. The most realistic scenario is a diurnally and seasonally constant low hydration state of zeolites controlled by the annual maximum surface temperature, in addition to a low abundance. Using these assumptions, the global distribution of the water content in the near-surface dry layer inferred from Mars Odyssey High-Energy Neutron Detector (HEND) data can be roughly explained. The best estimate of the zeolite abundance in the surface material to account for the observed water content is, on global average, ~30% for Ca-clinoptilolite, ~35% for Na-clinoptilolite, ~55% for K-clinoptilolite, and ~15% for chabazite if no other hydrated minerals are present. Putative regional confinement of zeolites to the dust-rich regions generally worsens the correlation between the modeled and observed water content compared with the scenario with globally uniform zeolite distribution, implying that zeolites may be present in dust-poor regions as well. In any case, our study shows that the diurnal atmospheric water cycle is unlikely to be affected by zeolites on the Martian surface.