合法滞在資格の審査中の扱いは州ごとに異なります。
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http://hidot.hawaii.gov/hawaiis-legal-presence-law/
Immigration has acknowledged receipt of my application. I am still waiting for my immigration documents to be processed. How will my pending status affect my eligibility to obtain a driver’s license?
Your DMV representative can review your documents and provide you with further assistance.
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ということで、I-485 pendingに関する書類をごっそりDMVへ持ち込んで、免許の当座延長を願い出ることになると思います。