Yes you can get brain damage from being on a ventilator.
Not everyone who has been on a ventilator has gotten brain damage but some people who have been on a ventilator longer than 20 to 30 days have experienced brain damage from being on the ventilator.
If the patient already has mental health issues and brain damage from other things then the chance of the brain damage increasing from being on a ventilator increases.
Some people who are on a ventilator recover fully and go on to live normal lives and some people come off the ventilator with mental problems due to slight to severe brain damage.
And some people die when taken off the ventilator.
It depends on how severe the health is of the person.