I went, in August 2013, on a polar bear viewing tour east of Churchill (alas, I didn't see any bears, it wasn't high season for them). I think we went east of the airport, so I probably clinched PR 636 on the tour's shuttle bus to the "tundra buggies" taking us into bear habitat.
That is, unless PR 636 also extends west of downtown Churchill (I saw no route signs in that direction). I walked a short distance west of town toward the port and its grain elevators, but couldn't cover much ground before I had to catch the train back to Thompson.
BTW, the rail line to Churchill is now closed indefinitely due to extensive trackbed damage. Until that's fixed, visitors to Churchill will need to get there by air.