If you're referring to an underaged applicant for OM (Trainee) status (who has at least one parent/legal guardian who is a non-retired OM), then yes, they have to submit a bucket-off photo, just like any other applicant. And, like any other applicant, all of their information submitted via their application is completely confidential.
If you're taking about applying to the Verd'ika Corps, that's actually its own organization with their own leadership and (presumably) some form of Approval Officers, and I don't have the answer regarding their procedures.