While mental/emotional issues are not uncommon in ALL the arts community, painters in general and impressionists specifically, are not prone to mental illness. Drug use and addiction is another matter. Alcohol and drug induced 'highs' are often justified as 'improving creativity and artistic genious'. So while its not true impressionists are or were all mentally ill, you may find a high frequency of alcoholism and drug use. But again in ALL fine arts not just impressionism. Ive heard more than one modern artist claim they just cant be 'creative' without being drunk or high.
Vincent Van Gogh was mentally ill but, while his illness may have contributed to his subject matter - namely his incessant obsession with self portraits - his illness had nothing to do with his skill as a painter nor the style he chose to paint in. Some artists enjoy realism. Others prefer a more impressionistic style. I looked up 'pointilism' the other day and was surprised to find Van Gogh listed. I can see why though. So he is now categorized as an impressionist and pointillist. Van Gogh was a truely gifted artist mentally ill or not. Remember impressionism was very avant garde for its big time period too so impressionists were the rebels who took a lot of abuse from art critics and the mainstream art world and were terribly underrated in their time Most did not get famous until after they had died. Most impressionists are not and were not mentally ill. Some had physical illnesses Renoir had rheumatiod arthritis and Manet had cataracts eventually. But mental illness was rare enough. They simply see the world a bit differently. The play of shadow and light and color of the world is simply visible to them, percieved by them, differently than realists. Different does not equate an illness.