I believe it is intended to be plugged in contnuously.
I think these devices only work with OBD data. The list of PIDs (https://en.wikipedia.org/wiki/OBD-II_PIDs) does not include economy in mpg. It does however have a fuel rate in litres per hour and odometer reading. Assuming your vehicle supports these PIDs, it will be the app receiving this data that will make a fuel economy calculation for you if it even has that as an option, I'm not sure.
Are you looking to monitor and adjust your driving style to minimise fuel consumption? You could just look at L/hr in that case.