Well, half of each sentence is correct this time. Nothing here actually makes sense, but there are numerous sentence fragments that are taken from the actual chemistry.
Alkaloids have nothing at all to do with bicarb.
All forms of chlorine in solution form hypochlorous acid, which is the chemical name for the disinfecting form of chlorine.
Positive hydrogen ions are always present in the water. They are not created by these reactions.
Hypochlorous acid bind to organics and for combined chlorines (there are several types). Additional chlorine binds with combined chlorine to break it down further. Again this is true for all forms of chlorine.
Sodium and carbon don't directly participate in these reactions, though they may be a part of the organic material that is reacting, or may simply be present in the water.
These reactions end up producing mostly water, salt, and nitrogen gas. Bicarb is not involved, either as a reactant or as a product.
Generally, if you "put a huge amount of sodium hypochloride in water that was full of organics" the water will clear up. However there are some (rare) situations where the water could cloud up, though this has nothing at all to do with bicarb. The most likely route for clouding up would happen because bleach is basic, i.e. raises the PH, and then lowers the PH as it breaks down. It is possible for that short period of high PH to cause calcium clouding.