No, the seas will not dry out. While local water bodies can shrink due to climate shifts or human diversion, the global ocean—covering 71% of Earth's surface—is a stable feature of our planet's hydrosphere.
Temporary recessions happen due to tides, seasonal evaporation, or local droughts, but these are fluctuations, not permanent drying. On geological timescales, ocean basins may change shape, but water remains abundant.