No, possums do not inhabit Vancouver Island. The only marsupial native to Canada is the Virginia opossum (Didelphis virginiana), and its established range is limited to southern Ontario and southern Quebec—thousands of kilometers east.
Several factors create this misconception:
The island hosts diverse placental mammals: black-tailed deer, Roosevelt elk, black bears, cougars, wolves, raccoons, and numerous small mammals—but no pouched mammals of any kind.
If you've seen a "possum" on Vancouver Island, it was likely a large rat, muskrat, or juvenile raccoon—common nocturnal foragers that can resemble opossums in dim light.