Of course, it's going to depend on how much interest rates go up. In my opinion, the interest rates we're expecting right now will likely not be high enough to bring on a correction in housing prices.
Some markets in Canada are overvalued right now. House prices are high compared to fundamentals, so rising interest rates will surely hurt demand.
It's important to keep in mind that this is really a marginal phenomenon. First-time homebuyers and those renewing their mortgages will be subject to higher interest rates, but the vast majority of Canadians have fixed-rate mortgages and will not experience higher mortgage rates for a certain amount of time.
All of this will nonetheless have a stabilizing effect. Also, keep in mind that most homeowners with mortgages are already qualified for loans with higher interest rates than they are paying right now. So that gives them some leeway to absorb rising mortgage rates.
In my opinion, this is really a marginal phenomenon that mostly applies to first-time buyers, who will be subject to higher mortgage rates.