Ignoring any kind of mercy rule that might be in effect...
"It is possible for time to expire during the throw-in following a successful free throw"
The clock is stopped during the free throw. The questions you have to answer are:
1. When does the clock start? 2. When does the throw-in end?
You already answered question 1. The answer to question 2 is:
NFHS 4-42 THROW-IN, THROWER, DESIGNATED SPOT
ART. 5 . . . The throw-in ends when:
a. The passed ball touches or is legally touched by another player inbounds.
b. The passed ball touches or is touched by another player out of bounds, except as in 7-5-7.
c. The throw-in team commits a throw-in violation.
So...if the clock doesn't start until it touches, or is legally touched by, a player on the court, and the throw-in ends at that same instant, I don't see how it's possible for time to expire during a throw-in. (Except at a couple of schools here where you have to keep your eye on the clock
)