Is it possible to fall asleep in the bath tub and drown?

Unlikely.....: It is possible for this to happen but unlikely since you would wake up once you were not breathing. Upon awakening, an adult would then be able to get their head above water, thus preventing drowning. However, if a person was under the influence of drugs or alcohol, then the normal reflex to awaken may be compromised making drowning more likely to occur.

Unlikely unless drug: It is unlikely your body's survival mechanisms would not kick in unless they are blunted by drugs which would depress the ability to "gasp" or to wake up, or to cough etc.