I'm using an LM386N in a simple amplifier and am using a 200uF cap parallel to the battery, before the switch, for noise supression. Should the cap (with no leakage) run the battery down in a week?
Well there will be some leakage so it will drain the battery to some extent which will be deturmined by the leakage current of the capacitor and the voltage and capacity of the battery. To avoid this your best bet is to put the switch before the capacitor so it's disconnected when it's not needed so it can't drain the battery.