powering +5v device with usb and/or battery
Regarding your first question, the block diagram doesn't really add anything to the discussion and it doesn't have enough detail to say whether it will work or not. For the benefit of readers who pay for their data I would suggest leaving it out, or drawing a proper diagram instead to taking a poor photo of a whiteboard.

As to the second question, the TI data sheet indicates that the converter will operate with input voltages from 1.8V to 5.5V. That suggests that you should be able to use it from 3.0V to 5.0V. If you have the PCB in hand, build it and find out.