I hope not; that depends on how the littoral states and populations will deal with ecological (especially pollution and environmental depletion), economical (water and waste management), health, financial (oil industries, conflicts), and with them social and political problems. As far as the irrigating rivers are not diverted, the Caspian Sea can "survive", provided that they can deal with the pollution and health issues.
https://en.wikipedia.org/wiki/Caspian_Sea
Sadly enough, human activities (agriculture, dams, industries, overexploitation) to develop the whole region destroyed the natural irrigation basin.
https://en.wikipedia.org/wiki/Aral_Sea