Does the clock stop on a PK in High School?

Yes

Here's the exact rule:

NFHS 2004-05 Soccer Rules Book
Rule 7 Duration of the Game and Length of Periods
Section 4 TIME-OUT AND IN
Art. 1 . . . The clock shall be stopped for a penalty kick, for cautioning (yellow card), for disqualifications (red card, yellow/red card), following the scoring of a goal and when a referee orders time-out.
Art. 2 . . . The clock shall be restarted when the ball is properly put into play.

NFHS RULES:

Because the clock restarts with a proper restart and a PK is not complete until the ball is out of play or its momentum is spent, a PK can continue past the end of a period. The clock restarts at the moment the ball is kicked and if time runs out before the ball reaches the goal, even if touched by the keeper, the goal counts.

That is the only time the clock expiration does not prevent a goal.

Right you are, Cecil.
Here's the rule clip:
7-1-4
"...A period shall end at the expiration of time.
EXCEPTION: Play shall be extended beyond the expiration of a period, in regulation time and overtime, to permit a penalty kick to be completed."