Same sex relationships seem to be given favourable treatment in some cases. For example, I have heard of conjugal cases being approved for a same sex couple in a scenario where there were absolutely no barriers to the couple living together or getting married while a straight couple would never in a million years have been approved with the same situation (both partners in this case had EU citizenship and would have had no problem living together in Europe, non-PR partner visa exempt to Canada, no barriers to getting married as a same sex couple in Canada or in various EU countries that allow it).
As for the original question about getting a visa extended to qualify for common law, I think if you say that you are planning to qualify for common law before you enter Canada, say while applying for a visa from outside Canada or even entering at the border, you might have a problem because there is a tendency to believe that such people will overstay.
However, once you are in Canada, you could already overstay whether they approve you or not so there is a tendency to approve extensions if you have a good reason. I remember a member on this forum saying they got 3 extensions approved, each time saying they were "exploring the relationship". Ok, maybe they got lucky getting that approved every time but saying that you are living in a common law relationship and will be applying for sponsorship in 6 months might well be approved, however, after 6 months, they'd like to see you really applying for sponsorship when you apply for the next extension. I also remember someone saying that they got one extension saying they were about to apply for sponsorship which they already qualified for but after 6 months, applying for another extension, not having applied for sponsorship yet, they were denied.