Most probably! Running burns adrenaline which is a real big part of many anxiety disorders, panic attacks etc. The less adrenaline you have spare, the better! Exercising/running in-turn should lead to more sleep/better quality of sleep.....which is widely praised as being of benefit to sufferers of mental illness.
The endorphins and endocannaboids (is that spelt right?) can certainly help with a person's sense of well being, not to mention self worth in some cases..
That said, whilst running can help with the symptoms of anxiety and probably depression too.......I'd say that finding the route cause of a person's mental condition is invariably important. Only then can a mental condition be worked on. For example, if someone has depression because they are overweight or gaining weight, running can be the perfect antidote.....happy hormones plus losing the weight!
However, if someone has low self esteem because....for example they were abused as a child or badly bullied as a teenager; running might help with some of the symptoms, but the real issues probably still need to be thrashed out with a mental health expert.