Yeah losing many thousands of young men to capture an island with diminished strategic importance may cause a bit of a continuity problem for the CCP leadership. Sure it’s useful for defending China from eastern invasion, but no one is invading China anytime soon.
Most will probably come from non-major cities and towns so I doubt it will be a problem. CCP knows they can take stuff pretty far. Probably only food production and fossil fuels are their chokepoints.