The latest research says "Yes!" This fantastic study out of my alma mater and previous employer, the University of Minnesota and its Carlson School of Management, looks at peer-to-peer influence and finds that people are 50% more likely to buy because of peer influence. Yes, they label the relationship as "causal." They also find that people with smaller numbers of friends are also more likely to be influenceable.
Great research, and this study is well worth your time.
Thank you to Andrew McAfee for sharing this study and a hat tip to the authors Ravi Bapna and Akhmed Umyarov for their hard work.