Actually, you don't need it to replace the SLA. The user code shuts the alarm off, and the display then tells you what the fault is and requires the user code again to reset the fault. So, remove the lid, shut the alarm off, but don't clear the tamper fault, and you have something 30 minutes before it times out and sounds the alarm again. Plenty of time in which to change the battery and get the lid back on.
Depends what you mean by "shut it down"?
The alarm does not have to be enabled -- it never is -- for it to trigger, if it thinks something is being tampered with; even when it obviously isn't.