No. It's very unlikely. A person might sleep for a number of hours, but the breathing is not affected so dying is extremely unlikely.
Agree w Dr. Andrew. Death from diphenhydramine overdose is not common. O/D sx's can include: Inability to urinate, Blurred vision, Dry mouth, Enlarged pupils, dry eyes, Ringing in ears, Low blood pressure, Rapid heart rate, Agitation, Confusion, Convulsions, Delirium, Depression, Drowsiness, Hallucinations, sleepiness, Nervousness, Tremor, Unsteadiness & Dry, red skin. Overdoses warrant urgent medical attention.