I doubt it. The provincial governments already run massive "health insurance" programs in Canada, this would not have been an impossible task to add a small dental program that only covers a fraction of the population to that.
Private "health insurance" cannot be cheaper than public. You have expenses which are the cost of people going to the dentist. And you have revenues, which are paid for through taxes. The only math that changes is that private insurance also adds profit for shareholders on top.
This is purely about privatizing Canadian healthcare.