Yes, you can get car insurance with a learner's permit or a school and work permit. The public interest is served by having all driver's have auto insurance, so state insurance commissions don't look too favorably on insurance companies if they refuse to insure permitted drivers. If you are under 18 you will likely need a parent on the policy with you as you are too young to sign a contract, but that is the only issue I have ever seen with a permit.
Let me know if you have more questions.