Yes, of course they will.
Blinking mode will also extend your life over solid mode.
The chip that runs the thing will take probably years to draw the battery down by itself; it's only the LEDs when they're on that draws any significant amount of current.
BTW, I've seen people mention that putting both banks in blinking mode may not be that good an idea; since they won't stay in sync, from very far away they look solid.
I ditched my LD1000 and am now using a Planet Bike SuperFlash, which as a bonus is cheaper.
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Work: the 8 hours that separates bike rides.