Yes. It seems counterintuitive, the idea being, for those who propose it, that you can take people waiting in line who have resources, move them into the private sector, get them off the rolls, and that will make both systems function well and the public system will be more efficient. But it's not true.
We cite a number of documented situations where that's happened in other jurisdictions: Australia, New Zealand, and Europe. What happens is that you move a whole lot of resources, such as physicians, nurses, and physiotherapists, out of the public system into private, for-profit care. The result is that those who can afford to pay—and our vulnerable population certainly can't—will get care sooner. For everybody left in line in the public system, the wait becomes longer.