I remember around 2010 and upwards, when people applied for PR (for context it took more than a year at that time to process the files), They usually do the medical as soon as they get their AOR in the mail ( Some were Paper based so you were patiently waiting for the post man to arrive
). The AOR confirms reception, and you have your application number. With that you can go to the doctor and do your medicals in order to have your application slightly faster done. Same thing with the payement of fees, some said if you pay everything together on the spot you'll win like a week in processing time.