It is not possible to just connect battery pack directly to GPIO, it would either kill Nano or would unable to deliver sufficient voltage, or both. When I had a need of something like this, at first I was thinking making my own device to solve the problem, but googling revealed that UPS for Jetson Nano already exists, and it does exactly that - powers Jetson Nano via GPIO, and if the barrel jack is unplugged, it will use batteries as a backup power source:
It works well for me. Its cut off voltage is 2.5V which is acceptable for modern Li-Ion batteries. Built-in LED fuel gauge is not accurate but fortunately remaining charge reported via I2C is of good accuracy. It is strange that they did not use values reported by i2c fuel gauge for built-in LED fuel gauge but other than that, everything works great. My Jetson Nano consumes at full load about 20W (instead of usual 10W) since it is overclocked (CPU 2.2GHz, GPU 1.2GHz, NVENC/NVDEC 0.8GHz), and input voltage (accorging to “sudo cat /sys/bus/i2c/drivers/ina3221x/6-0040/iio:device0/in_voltage0_input”) is within 4.79-4.81V at 20W power consumption. It would be better if they made it 5.25V instead of 5.1V so there is more voltage headroom under load (below 4.75V Jetson Nano can become unstable and some USB devices do not like USB voltage below 5.0V). But as of right now, this is the best UPS for Jetson Nano. And even when batteries about to hit 2.5V cut off threshold, input voltage is maintained at 4.8V@4A and there is no stability issues. I did not test if it can actually provide 8A while maintaining acceptable input voltage but it can provide at least 5-6A before input voltage hits 4.75V threshold which is good enough for me. It can simultaneously charge batteries and power nano. It has its own barrel jack socket, and the barrel jack socket at the Jetson Nano board is not supposed to be used, so I made a dummy plug for it to prevent its accidental usage instead of barrel jack socket of the UPS.