Can I add an INA219 voltage\current sensor to this USB powerbank?
Yes, the INA219 voltage/current sensing would be correctly applied directly at the battery cell terminal. This way you measure the current and the terminal voltage on the element that varies.
The current output (of the convertors) will not appreciably change until the unit is approaching failure so provides less predictive capability. 

You may need to consider reducing the current sensing R since the pulse currents from the battery to the convertors will be significantly higher than the output current. If you have too much Rsense then you will eventually restrict the pulse current and so alter the PWM. Read the INA219 datasheet to decide on a new Rsense and PGA value. It's likely that you will want to achieve less than 100mV Full scale Vsense.