Yes, if you are a listed driver on that policy and the carrier handles filings. The catch is that your record is then rated against every vehicle on the policy, which is why some families move the driver to their own policy instead.
More detail
This is the most common question from Lincoln and Kearney households, where student drivers sit on family policies. The mechanics are straightforward: the certificate is filed against the policy on which the driver is listed. The economics are not. A serious violation on a policy covering three vehicles surcharges all three, so the household cost of keeping the driver on the family policy can exceed the cost of a standalone policy in the driver name. Two alternatives are worth pricing rather than assuming: a separate policy for the flagged driver on the vehicle they actually use, and a driver exclusion on the family policy paired with their own coverage. Both are underwriting decisions, and both should be priced before anybody commits.