Yes and no.
Less severe mental illnesses like, say, anxiety can be alleviated through plain old EXPOSURE to what it is one is afraid of, & the symptoms of depression can be alleviated through physical exercise, meditation, various natural tools (CBT, for example).
So yes, there is the opportunity to recover.
More severe mental illnesses such as schizophrenia, bipolar disorder, psychosis... I don't think it is possible to be totally cured of these genuine brain abnormalities. These are primarily treated with medication, whereas not everyone with anxiety or depression need to utilize medication.
The scariest part of it all is analyzing the system we're currently in, where the mentally ill do not have effective care & access to sustainable treatment. Meanwhile, doctors are prescribing opioid medications to pain & post-surgery patients which are easily addictive, which is causing this current addiction crisis.
If these opiate medications are changing the wiring of the brain, & addiction is a disease (physical and/or mental illness), isn't this all just exacerbating the core issue at hand?
Anyway, I'm starting to meander, but it's worth thinking about. The effects of drugs themselves on mental illness are quite interesting, considering each drug affects each one of us differently.
In fact, if you have the genetic component for something like schizophrenia, the use of marijuana can actually exacerbate its dormancy.
It's a lot to think about. Makes me want to pick up a crack pipe just thinking about it.