The CFA is not 10% of your score. And the CFA is P/F. However, there is a small "bump" for doing really well and a small "ding" for barely skating by.
For the OP, the scores will almost certainly be passing, but barely on the mile. I think USNA will have concerns about the mile time. At USNA, males have to run 1.5 miles in 10:30 max. A 6:56 for one mile won't make that cut. As comparison, in my day, males had a 6:30 max time for one mile. Unless you're a runner who can really pace yourself, that last 1/2 mile is likely to be at a slower pace than the first mile. While the events before the mile run (plank and cadence push-ups) aren't as arduous as for the CFA, they will still tire you out.
Suggest you work on push ups and work on improving your mile time. Also, the CFA isn't viewed in a vacuum. If you are a star athlete in a non-running sport (i.e., swimming), they may not be so worried about your mile time. If you aren't super active in sports, the CFA is valued more highly as an indication of your fitness. So it could make a difference -- b/c the #2 reason for mids leaving USNA is failing to pass the 1.5 mile run. #1 BTW is leaving b/c you don't want to be there.