Not necessarily. It will depend on the area of specialisation that you pick. Psychology is not just about mental health. It is more about behaviour and all of us have specific behavioural patterns. Thus the training that you get as a psychologist will equip you to handle varied aspects of life such as family, education, human services, management, law and sports.
While psychology is generally applied in the diagnosis and treatment of mentally ill patients, it is also equally handy in normal everyday human/animal life – to understand the response and behaviour of consumers, students, work force, sports, even your own family members.
Psychologists are professionals are equipped with psychometric tests and tools to help identify a problem. Once they have identified it, they either help the patient overcome his inabilities through a few techniques or refer him or her to someone suitable for appropriate assistance.
However, if you choose to be a clinical psychologist, you might be interacting with a lot of patients who are mentally ill.