I was involved in a federal immigration study about 30 years ago, which came to the conclusion that, while immigrants were quick to adopt specific aspects of Canadian culture, most adult immigrants did not integrate fully, although the degree of the lack of integration depended on the degree of the original differences (i.e. an immigrant from India would be less integrated on average than an immigrant from the US, simply because the US immigrant was much closer to the Canadian culture to start with). Interestingly, the study also showed that the immigrant from the US was less likely to change his/her existing cultural differences to adapt to Canadian culture.
On the other hand, the study showed that the original immigrant’s children, especially Canadian-born children or ones who were quite young when they immigrated, were very likely to be fully integrated.
I don’t know how well these results stand now, considering that a much larger proportion of current immigrants to Canada are from Africa/Asia and are visibly as well as culturally different from the majority of Canadians.