That sounds highly unlikely. I don't know the details of your fuel gauging system, but typically there is a "sender" (more than one if the tank shape is complicated) of some kind in the tank - at its simplest this may be a float connected to a potentiometer giving a change in voltage as the float position changes - this voltage drives the indicator on the dashboard. To stop the dashboard indicator from swinging there will be some kind of damping arrangement - maybe mechanical on the indicator itself and a capacitor across the circuit to smooth out the voltage changes.
There will be a relay that trips the warning light on and off as the voltage level passes a threshold so it will be susceptible to exactly the same errors as the dashboard indicator.
Modern vehicles may have more sophisticated arrangements for transferring the information from the "sender" to the indicator, but the operating principles remain the same and the information is transferred continuously. Even if the use of a data bus and multiplexing results in discrete data packages, the switching frequency is relatively high and effectively the data are transferred in an unbroken stream.
Several of the components in the system, including simple wiring connections that oxydise, could account for what you are seeing and I would look first for simple solutions (like cleaning connections) . . . . . :)