You can do that, but you can't sign off on any documents as an engineer. You also won't eligible to write your P. Eng exam unless you've worked under a licensed engineer.
If this is true, it's changed in the last decade. I was able to write the engineering exam right out of school to become an "engineer in training". Becoming a full P. Eng required experience, but no exam.
it has indeed changed a little, I cannot explain as I was also under the last regime and also did not do that exam.