The 5V is provided by the internal switching buck converter on one of the DRV8301 chips. This provides up to 1.5A (7.5W) and is overload protected, and is specifically meant for powering external circuits. So yes, I think it should handle a RPi without problems (the worst it will do is drop out on overcurrent protection).
The onboard logic of the ODrive will be using something in the 10s of mA, I would guess.
However, if you are using the latest & greatest Pi with lots of USB peripherals attached, you might run into issues. They recommend PSU capacity up to 3.0A, because the Pi can supply up to 1.2A through USB, and will also use up to 1.8A itself if you load the CPU up to max. You might have to throttle back the maximum clock speed on the Pi or disable some cores.
Then again if it works off a standard USB port on your PC, it will be fine.