The short answer is a resounding NO.
While it might seem logical to reach for a powerful clog remover like Drano when your dishwasher is backing up with dirty water, doing so is dangerous, expensive, and potentially destructive. You should never use Drano, Liquid-Plumr, or any similar chemical drain cleaner in your dishwasher. can you use drano in a dishwasher
When in doubt, unplug the machine and call a professional. Your safety and your appliance depend on it. The short answer is a resounding NO