Being from Northern Ontario, I'd say the question kinda answers itself if you simply follow it by asking: which Canada?
Although Canada tends to be viewed as a homogeneously multicultural society (we all have our ideas of what any given country is like), Canada is (pardon my language) fucking huge. To ask for a novel to capture "the full sweep of Canadian life" is like asking for an American novel to somehow captures the essence of American life spanning California, Florida, New York, Texas, Utah, etc etc etc. America is best understood as union of otherwise unique states (you could call it... a united states). Canada is similar.
While you might reasonably expect a novel to capture the essence of living in France in a certain period of time, or in Spain, or in Italy, you could not reasonably expect a novel to capture all of the European experience. It's folly. And yet in Canada, we could fit most of Europe inside any one of our provinces or territories.
Canada may be a unified political entity, but it's not a unified cultural entity. There is a world of difference between the experience of growing up in Québec versus growing up in Alberta -- a difference as great as what I imagine it would be like to grow up in Utah versus New York, or Germany versus Britain.
It's a foolish idea to try and capture "the Canadian experience" because that experience doesn't exist. It's not a thing. Except maybe that it gets pretty cold in the winter and hockey is fairly universally liked for some reason.