No.
Remember, there are two axes to this thing. (More, really, but two will do.)
The Liberals are *socially liberal*. They are not "left" and never have been.
They have a core of people who believe in individual freedom and rights: equality for women and members of various minorities, resulting in support for reproductive and marriage choice, e.g.
Warren Allmand is an example of that core. He was "liberal" through and through. Throughout his career he was courted by the NDP, and of course maintained cordial relations on the left of the Liberals. I'll give him credit for his decision to stay in the Liberal party: he could not have been elected outside that party, and he was able to accomplish things by staying inside it.
The Liberal Party is right-wing economically and in other ways. The social liberals to some extent hold their noses on that part, and the right-wing elements tolerate the social liberals, although they themselves don't give a shit about their issues, or even outright oppose the "liberal" positions on things like choice and same-sex marriage.
In this way, the coalition that attracts votes from very different quarters, by holding up the right mirror to very different people, maintains itself and has reasonable success in getting and keeping power. Sometimes, in order to do that, the party, when in power, has to adopt positions from the left in order to stay in power, e.g. the social safety net arrangements that have been legislated by Liberal governments, under pressure from the NDP. Of course, this enables the Liberals to take credit for those achievements, thus attracting more votes from socially liberal / left-leaning voters.
The quick and easy illustration:
http://www.politicalcompass.org/canada2005http://www.politicalcompass.org/canada2008I was briefly a member of the Young Liberals too -- back around 1970-71. But we only did it because if we formed a campus Young Liberal club (there wasn't one where I was), the student council gave us money we could use for organizing our strike and other such things, and the Liberal Party paid our way to conventions. ;)