Not at the proof level needed for it to disinfect, at least not the earliest body piercings.

Alcohol is a disinfectant only at certain v/v percentages (or proof) - specifically between 60-90% (120-180 proof). 40% (such as vodka, whiskey, and most spirits) works in a pinch as well.

However the earliest alcohols were 10-15% ABV at most. We're talking about beers and wines that came from accidentally allowing fruits, bread, etc., ferment in water.

Now, mind you, even a 5-7% beer or winde won't have much microbial life in it, but that's because of constant exposure to an alcohol-ic environment.

Now, distillation for alcohol didn't come around until 1000CE-ish (distillation itself has been available since Ancient Mesopotamia, but was primarily used to clean water, or to concentrate perfume). Medieval monks were actually the first to distill wine into aqua vitae (a form of fortified wine)

So no, people ~2000 would not have had access to high enough potency alcohol to be used as a disinfectant.