CSA is an organization, therefore if CSA has not tested the design or reviewed the testing of the design, then its my understanding that the CSA mark cannot be applied (i.e. ,there is NO self declaration permission). Their ability to do a review only of the design testing may be limited by the test lab you used to do it and how CSA recognizes them (i.e. best case is that they are a CSA global partner).
Over and above product testing, CSA would require a factory registration and inspection regeime be in place before the CSA mark can be applied.
It's been a while (over 3 years) since I've worked with 60601 devices, but generally I recall CSA using 60601 with little to no national deviations.
Also, CSA can be a global mark (i.e., they are accredited to perform safety testing to several national safety standards).
If the Canadian market is your objective, CSA is not the only recognized mark. Other providers (UL, Intertek, etc.) can provide equivalent certification services to be compliant for Canada.
Best approach is to call CSA and get the specifics based on your needs and what you have for test reports.