You cannot use bleach to unclog a drain, according to slowdrain.org. It presents safety issues should you want to flush the pipe, use other products or take apart the drain.
When a drain is clogged, it contains extra water, which can dilute bleach. A blocked drain cannot be properly flushed, which is crucial for removing the chemical. Bleach may cause additional safety problems if the blocked pipe needs to be taken apart. If unclogging the pipe with bleach does not work, people sometimes decide to add other types of drain cleaner. Mixing bleach with these other chemicals can be dangerous.