If the student is not required to file a return, then the student would not report the 1099-Q.
See Do I Need to File a Tax Return? for guidance on whether your student must file.
There is no separate requirement to report Form 1099-Q; it only gets reported if the distribution exceeds qualifying expenses and then only if the resulting income meets the threshold for requiring a return.
As @MichaelDC states above, if the distribution doesn’t exceed the amount of the student's qualifying expenses, then you don't have to report any of the distribution as income on your tax return. If the distribution exceeds these expenses, then you must report the earnings on the excess as "other income" on your tax return. Unless the "other income" amount meets the filing threshold for the student, there is no requirement to file a return.
