This is untrue; the validity of your student visa has no bearing on your successful adjustment of status based on bona fide marriage to a U.S. citizen.
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I agree with my colleague.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
You are applying for adjustment of status, not naturalization. Naturalization pertains to the application for citizenship. You are not yet qualified for citizenship; you are currently applying for your conditional resident status. Your adjustment of status application will not be affected by the termination of your I-20.
As we all know, you must have meant adjustment of status, not naturalization. I agree with my colleague. Your school advisor is wrong. Since your I-485 case has been successfully filed and pending, even if your F-1 is terminated, you are not out of status until the decision is made. In other words, your green card case cannot be denied just because you fail to maintain your F-1 status.