Depends on what rules you are playing under concerning the balk and a pitch or throw:
You say tournament play; NFHS rules or OBR, makes a difference as you can see.
Under OBR, a balk is not dead, if a pitch or over throw ensues the play continues.
1. A balk and a pitch; balk is ignored only if; every runner and the batter advance at least one base, no option for the offense. EG; balk and a pitch with R3, long fly ball to CF, the ball is caught, batter did not reach 1st base, enforce the balk, award R3 home, batter back to the plate same count, no pitch. Near same scenario only ball falls in for base hit, R3 is thrown out at the plate, enforce the balk, though batter runner reached 1st R3 didn't advance also, R3 scores, batter back to the plate, same count, no pitch.
2. Balk and a throw: bases loaded, PO attempt at first, ball gets by F3 and rolls up the RF line, R3 & R2 score, but a confused R1 after diving back to first, finding the ball and scrambling for 2nd is thrown out by RF, enforce the balk, R3 scores, R2 back to third, R1 to second, all runners did not advance one base, no option.
I don't work FED, but everytime I go look; piaa_ump is right, so I believe him on.