First of all, the complaints system doesn't work quite like that. The charter is an instrument that is constitutional in nature, by which you can challenge specific provisions of an act of Parliament. Under the Human Rights Act what you would challenge is a discriminatory employment decision or a discriminatory failure to provide you with service because of your race.
Just with respect to that point, there was a decision by the Supreme Court of Canada, with all due respect to Justice Muldoon, in Gosselin v. Quebec in 2005, with the universal citation of SCC 15. It was a challenge to the Charter of the French Language, which essentially implemented section 23 of the charter about minority language rights.
What's relevant here is that the court didn't agree with the ability to challenge that statute, which was effectively using the charter.
In paragraph 14 they say the following:The linkage is fundamental to an understanding of the constitutional issue. Otherwise, for example, any legislation under s. 91(24) of the Constitution Act, 1867 (“Indians, and Lands reserved for the Indians”) would be vulnerable to attack as race-based inequality, and denominational school legislation could be pried loose from its constitutional base and attacked on the ground of religious discrimination. Such an approach would, in effect, nullify any exercise of the constitutional power:
So the suggestion there, what the court is saying, is that these acts are fundamentally connected to their constitutional base.