You don't have to control the whole A class shares, just some of the shares which drive the A share index.
It has been done before, in HK. The HK govt were using about 100B-150B US to fight off the attack on HK stock index during the Asia financial crisis in the late 90s.
From my contacts in CSRC, I was told China is growing aware and worried about foreign hot money plays the A share index. Thus the new regulations about delay the inclusion of certain price increases in index calculation.
Only time will tell how this all plays out...My sense is if there is smoke, there is fire.