Yes, that's precisely what it would probably do. One problem with all of these lines of argument is that you don't know exactly if voting behaviour is going to change with any change in rules.
We tend to talk about all systems, including that one, as if voting stays constant, and then we see what the outcome is. But voting doesn't always stay constant. One of the things we learned from Germany—this is getting off track—is that the Germans made some assumptions about voting when they invented MMP, and then about 20 years later, the parties discovered a different way to use it and began to pitch their campaigns differently, and voting behaviour began to change accordingly. So if you change the rules over some period of time, you might change behaviour.
If you gave Canadians second preferences, I think we could predict in the very short-term what would happen, because we can see what voting behaviour has been like recently. Maybe over a longer period it would produce some different outcomes. It's hard to know. But certainly, keep the party system constant, have voting behaviour and turnout much like the last election, and I think you can guess what would probably happen under AV.