False start can't be called once a play is under way. It's usually called before the ball is snapped, or as you mentioned, while the quarterback is taking his drop back into the pocket. In this case, the quarterback will spike the ball because he know's what the penalty is (he can see the offensive line better than anyone), or just wants to do so, just because he can.
The only penalty that will prevent the play from developing (or continuing to go on) is a false start. That has to be called immediately when it's seen. In the case of offsides, the officials will throw the flag, but won't kill the play. This is referred to in the NFL as a "free play" for the offense, because if they do something bad (e.g. throw an interception) it will be nullified by the offsides call. Aaron Rodgers of the Packers is a master of this.
They aren't flagged for intentional grounding because after a referee blows a whistle for false start, the play is dead - anything that happens after (like the quarterback throwing the ball into the ground) doesn't matter.