Is the battery being drained?
Is the battery being drained?


Yes. Yes it is. By it's internal self-discharge rate. See How do I calculate the self discharge rate of a lead acid battery? 
Nothing you can do about that, other than use the battery before it can discharge itself first.


  Which of these configurations (A or B) is better in terms of saving battery life (so that the battery lasts longer if there is never an intruder)


Neither is better.


  is there even a difference between the 2 configurations. I'm a newbie.


There is no difference. A disconnected series circuit is disconnected, no current can flow (not getting into high voltage and arcing across air gaps).