Is it possible for frustration stemming from avoidant personality disorder to lead to depression-like symptoms?

Absolutely: Avoidant personality causes stress and frustrations which can lead to depression and both can be comorbid. Different than schiziod which is similar but people want to be that way.

Definitely: People with personality disorders are more likely to have co-existing psychiatric disorders like depression, anxiety, psychosis, and substance issues. Sometimes we used medication to help with psychiatric symptoms while the patient continues therapy for the personality disorder.

Frustration : Yes, feelings of frustration, whatever they stem from can lead to feelings of depression. Mindfulness based stress reduction can help ease frustrations and give perspective to any life situation. As awareness and perspective increase, suffering and frustration decreases. Try this book: slowing down to the speed of life by richard carlson.