Short answer: I doubt it.
There are a few categories of people eligible for OHIP (Ontario health card); the ones that might apply to you are:
- "you are a foreign worker who holds a work permit valid for at least 6-months which permits you to work in Canada, and you are working under a formal agreement in place to work full-time for an employer situated in Ontario which sets out the employer's name, your occupation, and states that you will be working for no less than six consecutive months"
As you intend to work in Quebec, you won't get OHIP in this category.
- "you have submitted an application for permanent residence in Canada, and Citizenship and Immigration Canada has confirmed that you meet the eligibility requirements to apply for permanent residence in Canada"
For this purpose, the AOR does not count as a statement of eligibility. The "Request for RPRF and updates" probably does, but by this stage you almost have PR anyway.
Source - http://www.health.gov.on.ca/en/public/publications/ohip/temp_foreign.aspx
Source - http://www.health.gov.on.ca/en/public/programs/ohip/ohipfaq_mn.aspx