Can I submit my Canadian study permit online application without my?
Yes, but this will delay processing of your application. The consulate/embassy will send you a request to complete the medical and then set your file aside to check later to see if you did it. Getting an upfront medical will speed your application along. So, it all depends on how tight your timelines are if your want to wait for the embassy to ask or just get the medical done before applying. Your choice.