An employer can review a student's academic disciplinary record if the student authorizes as such. Educational records including disciplinary records and transcripts are protected under federal law, FERPA specifically, spelled FERPA. The federal law protects the disclosure of such records. A student would have to authorize such records to a given employer or prospective employer or whomever it would be.
That being said, if that's part of the application process or if an employer wants to see a student's disciplinary record, the student should not expect to be able to go further in the process if they refuse to do so. An employer cannot take steps to obtain the record on one's own but if that's part of the employment process then the student should expect to have to oblige in a sense of disclosing that record if, again, they're going to be seeking employment. That's why the consequences of an academic misconduct allegation can be severe. You need to make sure that you take the proper precautions so that your interests and rights are protected through the process so that you're not dealing with potential consequences both in the short and long term.