Generally, no. Bleach is a disinfectant and a bleaching agent, not a drain cleaner. It lacks the corrosive properties necessary to dissolve dense organic matter like human waste, toilet paper, or foreign objects.
If the toilet is not overflowing, this is the safest way to break up organic clogs. bleach clogged toilet
If the plunger fails, a toilet auger (a flexible coil with a crank handle) is designed specifically to navigate the S-trap of a toilet. It physically breaks up or hooks the obstruction to pull it back out. Generally, no