Taking Calcutta or Burma is the equivalent of taking Yunnan or Szechwan: No NO for China.
Unfortunately for the Chinese, if Calcutta or Burma is lost you will require Allied intervention to ever get that NO back.
AFAIK China can never leave its borders.
China can attack Burma, but not Calcutta. If Calcutta is taken by an axis power China has no chance getting NO by itself. It needs the help from another ally.