No. The Supreme Court of Canada has said that except in extremely rare circumstances, you can't do that—or not unless the legislation was amended. But I don't think that's the main point of testing. People get a little bent out of shape about testing, especially on the union side of the debate. The main point is to deter, to discourage, to say, “We don't want you to come to work under the influence, and by the way, you might be subject to a random test. You don't know when it's coming, so just don't do it. Please don't do it.”
But like the speeding sign on the 401 or 403 or wherever you're driving in Canada, it's not enough. You need to know that there's a police officer with a radar gun who might catch you randomly and say, “Slow down. Stop. And here's your reminder: please pay the ticket.”