The reaction neutralises itself almost immediately, producing mostly water, carbon dioxide and sodium acetate. There is no sustained chemical action and no mechanical force, which is what a real blockage requires.
As a monthly freshener for a bathroom basin, it is harmless and mildly useful. As an emergency fix for a blocked drain, it will cost you time you may not have.
If the water is not moving at all, skip the home remedies — clean the trap or get the run rodded or jetted.