Can you drink alcohol while having shingles and not taking any medication?

Within limits, i.e. moderate alcohol, there shouldn't be any problem. But why no treatment with an effective antiviral like valacyclovir? In addition to speeding healing, treatment reduces the chance of post-herpetic neuropathy, which can cause severe pain in the involved area.

No. Alcohol is a poison that never did anybody any good, ever, so stay away from it. It will destroy your brain cells, facilitate development of cancer in many organs, including breast, cause hepatitis, cirrhosis and pancreatitis etc. There is no safe level of alcohol intake. Quit while you are ahead.