Should i pull the crown to save battery if i store my quartz watch for a few months

First of all, a watch battery can be changed for under $5 in many cases. That said, why would you want to "pause" the movement? It isn't worth the possible damage and most likely the battery consumption is so low that the batterie's expiration date will not be affected at all. Not worth the possible malfunction.

I don't think storing a watch with the crown out accomplishes much. That I am aware of, pulling the crown out does not break the electrical connection between the battery and the watch. At least in looking at quartz movements, I don't see any electrical apparatus that insulates the crown in any way so that it could act as a switch. I think that in quartz watches that hack, pulling the crown out mechanically disengages or interferes with the drive train, but it doesn't stop the oscillator or stepper motor from running.
With quartz movements, at least those I have seen the internals of, (most ETA and ISA designs, some Rondas, a few Seikos), pulling the crown to the setting position does one of two things:
1) On better, jeweled movements - it breaks contact between the coil and battery, thus stopping the motor. The oscilator continues to be powered, but most of the current consumption is from the motor. These pulling the crown out does save battery life. Or,

2) On cheaper non-jeweled movements - it blocks the rotation of the second hand gear, and stalls the motor. These are observable by a "twitchy" second hand when the stem is out. This method actually kills the battery faster, as a stalled electric motor draws more current.