Thin white envelope?

You won't get a TWE. You will get an update on your portal that says something like "Denied" or 'Turned Down" in the little box.
Don't hold out hope for actual mail from USNA if you are being turned down.

And it may not happen until mid-April.
As a general rule (there can be exceptions), turndowns are rolled out in the following order:

1. Candidates who did not complete 100% of their package.
2. Candidates with completed package without a nomination who will not be offered NAPS/Foundation.
3. Candidates with completed package and one or more noms.

The last group are typically those who won't hear until somewhat late in the process (closer to April 15 than Feb. 1).