Medical passed since December 1st, 2020. No DM, No COPR since then. I don't think doing Upfront medical actually help catalyse the process.
My friend who got MR request and passed Jan 11 received COPR yesterday. Same BCPNP.
I would advise that if you can wait for MR, please wait for it. it will definitely worth it. Doing Upfront medical makes absolutely no difference.
My personal opinion
As I mentioned before, upfront medical did have difference depends on where you live. In Vancouver, the labs are pretty busy. The earliest one you can book will be weeks after. So if you wait until you got the medical request then go to book for the medical exam, you have to wait for a couple more weeks or even a month. Then it will take another week for the lab to process your medical exam result and upload it to CIC. In total, there will be around a month of delay after you got your MR and do the medical compares with upfront.
Other than that, there is no offical statement that claims the upfront medical can speed up your process, or not. So I don't think anyone can deny the possibility. If you compare it with the upfront PRPF where the official site claimed that it will delay your process if you didn't pay your fee upfront, then doing upfront will also kind of speed the process up a bit I believe.
The only downside of upfront medical is, if you did it too early or the process takes too long, it may expired before the application is completed. That's $300 or so wasted of money. However, the lab fee and X-ray can be reimbursed by the work insurance. That's around $100 only.