Per AR 40-501, current (or a history of) high blood pressure is disqualifying. That doesn't mean a waiver is impossible, but expect to be DQ'd and have to go through the process. Best of luck to your son.
The Reg:
Current or history of hypertensive vascular disease (401) does not meet the standard. Elevated blood pressure defined as the average of three consecutive sitting blood pressure measurements separated by at least 10 minutes, diastolic greater than 90 mmHg or three consecutive systolic pressure measurements greater than 140 mmHg does not meet the standard (796.2).