aarg:
I'm curious - I noticed an unpopulated place for 32khz crystal and trim caps on my Due board. I wondered about whether you could populate and run it. Why would it be completely not allowed? What kills the idea?
Then your Due probably can run the RTC module on the chip. All the Due boards I have don't have any spare pads for the crystal.
Adding the coin cell battery to the Due to keep the clock running when the rest of the chip is not running is also an issue to be checked. The original Due design doesn't allow those pins to be powered without powering the rest of the chip.