Answer: Not in this situation. Since this student has been in a stable home with her grandparents since 5th grade, she does not qualify as homeless under the McKinney-Vento Act. (We are assuming the housing is adequate.) It would not be appropriate for you to provide a verification letter to the university, since the student is not homeless.
However, the local university can do a dependency override for special circumstances for this student. The financial aid office would handle that, working directly with the grandmother and the student to make the determination. You could offer to the grandmother to call the financial aid office to discuss the situation, if the grandmother consents to you providing that support and information.