If you do it now, will the information be true, as in the most distinct meaning of true? It is indeed a superb and worthwhile distinction to report when you are.
To educate myself, I read this:
It seems to me you must successfully pass this last hurdle before you can call yourself an Eagle Scout. Is that how you read it? Would you be “rounding up” an achievement? Either you are or you aren’t one as of this moment, and you know which you are, and you know the right people in your Scout organization to ask when you can report your status. No need to get unofficial advice from an anonymous Internet forum!
Have you approached your school counselor and respectfully asked if they would be willing to update this for you the minute you know, even during their break? If they decline, then thank them and figure you tried. Admissions will likely be lightly staffed during this period except on actual holidays, so some work will be ongoing.
Alternately, be prepared to leap on this task the minute it is practicable.