Do drugs affect mental health

This heavily depends on what specific drug you are talking about. Something like aspirin is unlikely to do so, however many drugs may certainly be psychoactive.

Some drugs are specifically used to affect the brain function. They are used to treat conditions like depression and schizophrenia. Some other drugs have psychoactive properties as side effects.

Drugs used recreationally can also affect mental health, especially in people predisposed to mental illness. For instance, alcohol abuse is well known to cause some conditions and make others worse.