In my case I did e-Medicals upfront. I have no idea if that will speed up the total processing time though, but apparently it speeds up medicals processing. Just make sure it's upfront e-Medicals, not just Upfront medicals (I heard there's a difference).
You can do upfront e-Medicals at any time during your application processing starting with booking an appointment with any of the doctors from the IRCC list. All you need is your passport or national ID (in my case - Canadian driver's license).
My timeline:
SK Inland (with Job Offer)
Appl received: Jan 6, 2016
AOR: March 17, 2016
e-Medicals: December 19, 2016
MR: January 14, 2017
Medicals "passed": January 17, 2017