Most car insurance companies like to know everyone who is of driving age and has a license to be either listed on the policy or excluded. To them, it's simply peace of mind so they're aware of all the risks presented to them.
While I do not work for Farmers, it has been my experience that they do allow exclusions. Usually, you will need to call your agent or a customer service representation at their call sent and request an exclusion form.
The decision will ultimately be determined by the policy rules of your insurance company. Because he won't be driving for 6 months but is of driving age, your best bet would be to see if you could "exclude" him from your policy for the duration of his suspension.
Although you technically do not have insurance, the other driver is still at-fault for the damages and thus has a legal obligation to pay for the damages caused. You might be ticketed for driving without insurance but that shouldn't impact your parent's ability to have the other driver pay for the damages.