Can anxiety be fatal?

Usually not: Anxiety, in and of itself, is not a fatal disease. It does have physical manifestations, but those are not life threatening. On the other hand, people are anxious are at higher risk for traumas, as they may lose control over their actions when anxious and do things that they would not normally do.

Anxiety: No, however it can be debilitating, exhausting, and usually is associated with depression. The good news is that there are many, many treatments for anxiety, including behavioral and pharmaceutical.

Eventually only: It's a very slow (usually many decades) and painful way to die. The acute anxiety/panic attacks may feel like you're dying, but almost never do kill anyone. It's the long-term damage wrecked on your body by excess exposure to stress hormones that eventually does us in. Also the hazardous risk-taking, abusive behaviors many do to react to anxiety. The death certificate will not say "Anxiety".