Several years ago, the CFA could be submitted later than the rest of the package. That is no longer the case -- it is due by Jan. 31. If you fail, you should contact your Regional Director and find out if there are any other options.
As a general matter, not only is USNA not likely to permit you to submit it late, there's little practical benefit in allowing you to do so. Some possible reasons that they might permit a late submission: (1) a long-term injury that has prevented you from taking/passing the test; or (2) being a candidate they really, really want who is barely failing one element but doing really, really well on the other elements.
I'm not saying USNA would permit a late submission but also suggesting there could be a set of facts that would permit it. That said, if you wait until the last minute and fail -- especially if the failure is severe in one or more areas -- the chances you can significantly improve in a week or two is very slim.
For those applying for the Class of 2022, prepare early, take the test early (as in June - Sept) and then, if you have areas in which to improve, you have 4-5 months to do so.