Is it safe to take vicodin for back pain after drinking three beers?

No. Alcohol and hydrocodone are both central nervous system depressants (cns depressants). This means they both can slow the functioning of the brain. Importantly, both hydrocodone and alcohol can cause respiratory depression (shallow or infrequent breathing). Drinking alcohol while taking hydrocodone may increase your risk for serious reactions.
No. Vicodin (hydrocodone) is a narcotic medication and by definition it slows down the function of the central nervous system. The short answer is alcohol and central nervous depressants should not be mixed.