no. must be a resident to buy auto insurance. a state license is required.
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Yes you can buy auto insurance using you international driving licence. I know this because i have done it. Just call up an insurance broaker, tell them your situation and they can usually help. As far as i know State Farm are the only ones that require a State Licence.
We are from Norway and have insurance through Progressive for our automobile and our travel trailer. You can fill everything out on-line and receive your policy information, proof of insurance (card) and everything in the mail. (we have a U.S. mailing address)