Well, you could contact USNA and get "prior permission" I suppose. The Body Alteration Form isn't explicit as to how to go about getting that permission, however.
Stories or rumors about what you can and cannot do, are not something you should put any stock into.
Recent SAF threads concerning tattoos also either dealt with getting them before an Offer of Appointment was received, or from an ROTC standpoint.
Both of those scenarios are different from your situation.
Considering that you already have an Offer of Appointment and have sent in the first three items (Police Record Check, Body Alteration Form, and Proof of Citizenship), the next thing you
will receive is the Permit To Report (PTR) package, which contains a litany of other forms and information required on or before I-Day.
Last year's PTR package clearly stated;
"Any candidate who reports with a tattoo, brand, or body piercing which does conform to our policy, who has not been cleared through the procedure explained in our correspondence, or has not contacted the Director, Nominations and Appointments should anticipate not being inducted into the Brigade."