It's kind of a complicated question to answer, because the term itself has such buried meaning, you'd be hard pressed to find many who even know what it means these days. But, let's go with the standard definition, as provided by the Oxford dictionary:
If you accept this definition, then the answer is kind of muddled; yes, but no. The Liberal Party was historically born out of the Radical Reformers of the mid-to-late 19th Century, who did ostensibly promote reform of Canada's social values, alongside the civic and government systems that kept the nation running. And throughout the history of the country, the Liberals usually fell on the path of reforming Canada's laws for social and civic reform, though not always. But it can also be said that the Conservatives were relatively progressive as well, including under the reign of John A. MacDonald, who built the country, through to Diefenbaker, who introduced the original Bill of Rights. In a way, quite a lot of Canada's governments have been progressive in some form or another, if you follow this definition.
"(of a person or idea) favouring social reform"
There's other, more political definitions of "progressive" as well, most of them centering on the idea that one must support continuous change by the government to meet society's demands as culture, infrastructure, diversity, and general ideas evolve. In this way, it's possible to say that the Liberals are generally progressive, but in many specific instances, they are not.
The idea surrounding this apparent conflict is simple: the Liberals will generally shift with a population's views, but will also heartily defend the status quo when it views the status quo as the more reasonable option, compared to the evolving demands of the population.
What constitutes a "reasonable option"? Either the idea that it grinds against Liberal values in government, or it grinds against advantageous perks Liberals tend to rely on. Most often, it's a combination of both (as it is for all political parties).
The best example is probably the Senate. The vast majority of Canadians are not in favour of the Senate as it currently stands, but the Liberals have been the ones to defend how it works. Why is that? A lot of it has to do with attachment to the traditions of Parliament, something the Liberals are known for. A lot of it also has to do with the fact that Liberals could appoint their own men and women there out of patronage and political necessity.
However, in general, most Liberals will say that something needs to be done. Almost all Liberal Prime Ministers have made some sort of change to the Senate, but nothing that would upset the status quo. In this way, Liberals generally support the idea, but specifically they're sticking with the status quo, making only minor changes when they can.
You'll find this sort of theme throughout the Liberal Party's entire history of ideas, from gay rights to the Constitution to general government services. As a rule, the Liberals are supportive of reform, but they will do it in baby steps. This was also the rule for the Progressive Conservatives, though their baby steps took a little longer. The NDP, never having been in government except in the provinces, haven't had much of a chance to show what they'd do and how they'd do it; one can point to Tommy Douglas, but even he did some piecemeal reform, and some of his ideas, at least personally, were not very progressive. The other NDP Premiers generally aren't worth mentioning, due to their lack of record in government, or general inclination to Red Dipperism.
Taking all of this into account, the reality is that the Liberals are, in practice, supportive of the status-quo, even in the face of evolving demands of society, making them not extremely progressive. This is something true of most ideologically similar parties to the Liberals, as well.
But, before anyone reads too much into that, here's the caveat - progressive doesn't really mean anything. As I said at the beginning, you'd be very hard pressed to find a definition that everyone agree's on. Indeed, to a point its been co-opted by leftist parties like the NDP or Greens, despite the fact that the Conservatives, once upon a time, were a very progressive party despite being right-wing in ideology.
If one says that all left-wing parties or persons are "progressives," then a lot of the Liberals would indeed be "progressives," as would much of their social, civic, and economic policy. Of course, this is a very selective outlook, and one has to think the Liberals are left-wing in order to assume that they're progressives. One way or the other, or both ways in fact, they'd be committing a fallacy in terms of getting a bastardized definition of what it means to be progressive politically.
This is why, in general, I try and avoid the use of the term "progressive." Yes, I'm on ProgBlogs, but the term is pretty much fluid from what I've seen. What really constitutes someone, or some party, as "progressive"? I'm sure I'm not progressive in the eyes of some people; after all, I support many economic policies that are somewhat to the right economically that other so-called "progressives" are absolutely vapid against. Then again, I support a lot of social reforms and policies that are left-wing and would earn me a spot right beside some of those same people. And I do support general government reform, but not too much of it.
And if I'm a typical Canadian citizen or Liberal voter, what does that make me, the country, and the Party? Progressive or reactionary? If you figure the definition out, you'll get your answer to all three.