The current ruling is that they activate at the end of the draw. If you draw Destruction/Shrink (the CoW Soul that discards an Enhancement) off Reach, you can discard the interrupted Enhancement before the play.
The alternative probably treats "if drawn" and similar clauses as triggers, so LS activate at the end of the draw but you can't use the triggers until after the play, which means LS that are just active (Protection, Negates, Modifiers) are active during the play, but those with triggers are delayed. Which sounds really complicated.
