Yes, but it depends on the issue.
Permanent residents would not have Canadian citizenship and the consular services are essentially predicated on citizenship, but there have been any number of situations around the world involving permanent residents in which we have reached in. If the local government is willing to co-operate with us, then we try to provide whatever assistance they would find acceptable.
Back in 1994 in Rwanda, we had one situation in which we had nuns who were running an orphanage in Kigali, and we got them all the way out, with the kids, to Nairobi. We then got them on a plane, and they all ended up in Quebec City. None of them were Canadian citizens, but we do this sort of thing for humanitarian reasons in these situations.