Mike - don't think so as I assume your gauge in the console is using the same ground as the low fuel monitor is.
But the low fuel monitor should be getting the same oms from the tank sender and report the same levels as the gauge.
That's why it is important to test the gauge, the tank sender, and the low fuel monitor. If you get 45ohms (1/2 a tank) at the sender, and the gauge and you test the monitor and get less then 45 the wiring or the monitor itself would be suspect. Your base line test of the sender lead in the trunk will be the only standard, assuming you KNOW how much fuel is really in the tank.
Here is a troubleshooting I wrote over on TC http://www.camaros.net/forums/showpost.php?p=1579191&postcount=2
see if that helps you run the tests.