Yes, it is possible. It's somewhat uncommon, but totally possible.

Benzodiazepine overdose describes the ingestion of one of the drugs in thebenzodiazepine class in quantities greater than are recommended or generally practiced. The most common symptoms ofoverdose include central nervous system(CNS) depression, impaired balance, ataxia, and slurred speech. Severe symptoms include coma and respiratory depression. Supportive care is the mainstay of treatment of benzodiazepine overdose. There is an antidote, flumazenil, but its use is controversial.[1]

Benzodiazepine overdose

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Death from single-drug benzodiazepine overdoses occur infrequently,[2] particularly after the point of hospital admission.[3]However, combinations of high doses of benzodiazepines with alcohol, barbiturates,opioids or tricyclic antidepressants are particularly dangerous, and may lead to severe complications such as coma or death. In 2013, benzodiazepines were involved in 31% of the estimated 22,767 deaths from prescription drug overdose in the United States.[4] The US Food and Drug Administration (FDA) has subsequently issued a black box warning regarding concurrent use of benzodiazepines and opioids.[5] Benzodiazepines are one of the most highly prescribed classes of drugs,[6]and they are commonly used in self-poisoning.[7][8]