Based on your timeline I suppose you have already decided what to do but I thought I would give my 2 cents anyways. One of the things I do for a living is write HR policy so I have some familiarity with the subject.

It is a violation of privacy but as you say refusal may not be recieved well. It is also true that you can be dismissed within your probationary period without cause. Your employment contract likely sets out in the terms that it is subject to successful completion of the probationary period. This means they can hide discrimination because they don't need to give a reason for releasing you before your probation is up. It's a catch 22.

Were I in your shoes I would likely go ahead and disclose and take the risk. If they dismiss me because of my disclosure then perhaps it isn't a good fit for me. If I do need accommodation I want to know my organization will actually come through for me. Their response to my disclosure will be a good early indicator.

Being willing to battle stigma is a worthy cause and more of us need to be willing to do the work and take the risks that that involves. It isn't easy but the more people are exposed to people with mental illness functioning the more likely the stigmas can be torn down.

If you refuse to sign, when your probationary period is over and if you find yourself in need of accommodation you can still get it based on the current need without having disclosed any related history. Accommodation is legislated by our Canadian labour law and they would be hard pressed to refuse you.

Curious to hear what you decided.