No, typically your parent’s insurance will not increase when you have a G1 licence as this is only a learner’s permit. Your parents will need to let their insurance company know though that you’ve got your G1 licence, but their premiums won’t change until you get your G2 licence. Each time you move through the graduated licensing system (getting your G1, G2 and then being fully licensed) your parents must notify their insurer.
The reason getting your G1 doesn’t affect your parent’s insurance is because a G1 learner’s permit is just that–a learner’s permit. It is the first level in Ontario’s graduated licensing program. It is a highly restrictive licence, with many conditions one of which is that the G1 driver must never drive alone. Another fully licensed driver (who is sober, has at least four years of driving experience, and whose licence is not suspended) must be sitting in the front passenger seat of the car, supervising the G1 driver.
It’s when you can drive solo—without a supervisor—that your parent’s insurance premiums will increase.