Is it true that drinking (even a little bit) when you're a teen can cause alcoholism later in life?

No. No, there is no reason that small alcohol experience in teenage years will cause alcoholism.
No. Drinking a little bit or as is done in certain cultures doesn't lead to alcoholism. Recurrent use of alcohol and/or drugs to relieve anxiety as a teen can prevent the child from learning appropriate coping skills and lead to further addictive behavior.