A few years ago, the Secretary of the Treasury Board at the time told me that 40% of new public servants were already bilingual when they were hired. I would assume, then, that a significant portion of those new employees are the product of immersion programs, but not all.
Myself, I am not the product of an immersion program. If there's anything negative about the success of immersion programs, it's the misconception that they're the only way to learn French. Clearly, that's not the case. I know many people who are perfectly at ease in both official languages and who did not go through immersion programs. They learned the other language later in life, as I did.