The hose connecting the dishwasher to the sink/disposal can get kinked or clogged.
The most immediate risk is to the rubber and plastic components. Sodium hydroxide is highly corrosive to many plastics and elastomers commonly used in dishwasher seals, gaskets, and drain hoses. The intense heat generated by Drano’s reaction can soften, warp, or melt these parts, causing immediate leaks or catastrophic failure of the drain pump. Furthermore, the bubbling action and hydrogen gas release, while useful in a vertical drain, can cause foam to erupt from the dishwasher’s vents and door seals, creating a dangerous, caustic spray in the kitchen.