If there's no pullup resistor on that line on the module, then you can configure the GPIO as INPUT_PULLUP. And then you can power down the module's Vcc pin, but the alarm will still work. But if there's a pullup on the module tied to the module's Vcc, then you have to keep Vcc high while waiting for the alarm to trigger. The DS3231 uses about 50 times more power running on Vcc than it does running on the coin battery, so you want to power it down when you can. The coin cell will still last a long time.
It just seems they could have connected pin 4 to something - anything that might be useful - rather than leaving it NC. And the most useful thing would be the alarm pin.
Probably, trying to make it fit on certain pins on the PI I/O header with a minimum of worry about how those pins are configured. It's specifically designed to fit the PI.
BTW, good luck finding a replacement battery if yours runs out. At least, where I live... and it's hard to mail order batteries in many cases due to postal restrictions.
If one of those units sat on the shelf for a while before you bought it, the internal oscillator was running, and the battery is often already weak.
If it wasn't hobby grade, the manufacturer could disable the oscillator for storage/shipment, but that isn't possible because hobby software doesn't look at that control bit, so it makes the unit appear defective. That isn't an issue with most boards, because a battery replacement resets the bit. But this one is soldered in.
Once it's doing its job as a backup, the battery is of course not under load, so everything is fine. But it's too tiny to run the IC stand alone for extended periods of time.
My experience with those boards, and some similar ones that had tab soldered batteries on board, is that the batteries were dead after about one year of storage.