Due to timing, I suspect USNA doesn't even see many candidates 7th Semester grades before making Admissions decisions. However, you are playing with fire here.. First, I would expect USNA reviews the entire transcript before I-Day, and would question any significant drop in grades. (Perhaps a current parent can comment on how the Offer of Appointment is worded -- I would expect it to be contingent upon continued performance, staying out of trouble, medical , etc). Second, I really don't think one can "prepare" for the SAT/ACT in a week, so candidate might be shooting him/herself in the foot without any gain.
Needless to say. not a good position to be in and not the right way to prepare for entry into USNA. One of keys to success at USNA is the ability to manage time, anticipating demands and prioritizing. Getting backed into a corner like this at USNA will result in a snowballing effect. Bottom line, you have to figure a way to do everything, and do it well.