"Can alcohol cause permanent anxiety even after sobriety?"
I believe that question is the result of anxiety and asking ourselves that question will cause more anxiety, its a catch 22. Thats how it works, its the worry of worry, the fear of fear.
I have had anxiety my entire life and drank it away for 6 years. It got worse when I quit drinking but now is getting much better due to the lack of alcohol and the fact that I am changing the way I look at situations, diet, exercise, facing my fears and gaining confidence every step I take.
I have yet to read anywhere proof of "permanent" anxiety from alcohol or drug abuse. Its simply not true. Its a LEARNED behavior that can be changed. It takes time and knowledge.