Not necessarily...you can have a foul after the clock hits 0.00 and still have no time on the clock if the ball is released in time, and the foul is on an airborne shooter.

In a perfect world, yes if you had a foul then horn, you would add time back on the clock. You see this in all NBA games and most major D-I NCAA games where they have the benefit of replay. Your state association has determined there must be .3 seconds added to the clock if this situation occurs, but that's an arbitrary number as there could be less time on the lock.

We don't actually mandate .03 on the clock...just "time"... I can't argue arbitrary :)

Yes, zero's on the clock with a foul is an instant replay trigger...so in that case you'll more than likely put time on the clock though you COULD shoot free throws with no time on the clock if a foul after time expired is committed against a player in the act of shooting and the ball is released before time expires.

For clarification
 

NBA Rules
5-III a. Exceptions (2)

Yes time will be added on if the whistle is for a foul that is prior to the zeros on the clock.

NBA Case Book (2010-2011)

142. Player A1 is fouled in the act of shooting by Player B1 with :00.0 remaining on the game clock. The game is in the fourth period and the score is tied. What is the procedure?

The officials must go to instant replay to see if the foul occurred with time remaining on the clock. If so, Player A1 will be awarded free throw attempts and time will be placed back on the clock according to the replay. If the foul occurs after the clock expired and the player was still in his shooting motion, the officials must determine that the ball was released before the clock expired and if so, free throws will be administered accordingly. If the game clock expires before the ball is released, no common foul can be administered since the period has technically ended.
RULE 13 - SECTION I - a (2)
RULE 13 - SECTION II - b

187. Player A1 is fouled just as he releases the ball on a field goal attempt and the horn sounds to end the period at approximately the same time. How is this administered?

The officials will utilize instant replay to determine if the foul occurred prior to the expiration of time. If so, the game clock should be reset to the time of the foul and free throws administered accordingly. If the foul occurred after the clock expired and the player was still in his shooting motion, the officials must determine that the ball was released before the clock expired and if so, free throws will be administered accordingly. If the clock expired before the ball was released, no common foul can be administered since the period has technically ended.
RULE 4 - SECTION X
RULE 13 - SECTION II - a (2) and b (2)