This is a complicated question. The short answer is that mental health, including addiction, still qualifies under the grounds of disability. If you do find yourself struggling with your mental health (as millions of Canadians do) and need accommodation, you should be able to approach your manager or employer and hopefully come up with some solutions or options before the problem gets worse. Your employer might also be able to lead you towards an Employee Assistance Program, which is included in many extended benefit plans, and may provide mental health counselling or resources for addiction treatment. If you are being criticized or disciplined for performance issues that relate to a disability, it would be wise to pre-empt further discipline by disclosing that.
The unique feature though when mental health and addiction are involved is that it does not need to be the employee who comes forward first. If your employer sees that you are really struggling, and gets the sense that there may be a mental health issue, they actually have a legal duty to inquire and ask if you are alright or could use any help. Mental health is not always as obvious as a broken leg, and shame and stigma too often stops people from coming forward.
Employers should ask if they see you struggling, and should try to connect you with available resources. They are not, however, therapists or social workers. If they make an inquiry, and you adamantly refuse help, then they can only be expected to proceed as normal.