Will binge drinking on the weekends make my immune system weak and prevent it from clearing my genital warts on their own?

Drinking excess alcohol does suppress immune system. It would affect your body’s natural immunity and response to all kinds of infections.

Genital warts can go away on their own as the immune system fights off the infection that causes it (although they sometimes don’t go away on their own, and they also sometimes come back.) Excessive alcohol consumption can weaken the immune system and can blunt recovery from infections, so while it may have no impact at all, it’s possible they may make genital wart disappearance less likely.