The T4 has a 12V input so unless you can create a battery system with a 12V output, you are stuck. The design of the board prohibits direct connection of 5V to the GPIO headers, unlike some of the other boards.
The PMIC used does not support a battery either.
GPS and accelerometer can be connected via USB for GPS and I2C for the accelerometer. You will likely have to develop your own driver for them unless you can hack the kernel to add them if the source already exists.