If a child is bullied more as a kid are they more likely to abuse alcohol as an adult?

Perhaps. Bullies, and those who are bullied, are more at risk for many emotional health problems later on. Many people try to self-treat their emotional pain with substances like alcohol. There are many other factors that also influence the risk of adult alcohol abuse, including family history of alcohol or drug abuse, personal characteristics of vulnerability vs. Resilience, social support, or lack of it.
Vulnerability. How a child, parents and society deal with bullying affects the psychological outcome on the child. Children who are made to feel helpless and vulnerable by the bullying are more likely to develop anxiety and depression and ultimately alcohol abuse. With family and school support the victim can be helped to feel empowered reducing the risk of future psychological disorders.