The module and development board uses DC DC converters, which means they draw more current if the voltage is lower.
The module is specified as 5.5V minimum. I imagine that any conforming power control circuitry will assert power bad and shut down if the voltage goes below that.
If you’re using a LiPo straight into the Jetson, I suggest you use a “low battery alarm” to save the battery from over-discharge; LiPos discharged below 3.0V per cell are dangerous to recharge and dangerous to use after re-charge (and, in fact, if they over-discharge, you may not be able to re-charge them at all, even if you’re willing to live dangerously.)
For example: Amazon.com