It MAY work with the stock sender, though the readings may not be exact. Better to use the sensor that came with the gauge.
What will not work is to leave the factory gauge connected while you 'tap in' the aftermarket.
The sensor is basically a variable resistor, where the resistance decreases as temperature increases. The gauges both send a constant voltage, and measure current over the circuit in order to position the gauge. So the gauge itself is an ammeter. The stock gauge has resistance, so it cannot react very quickly as its major fault. Anyway, when you have 2 voltage sources, it screws up the current measurement, especially if one of the gauges uses a resistor divider network to calibrate its voltage source. I believe that the stock gauge does this. This means that there are multiple paths to ground for the other gauge, which messes it up badly.
Still, the best solution is to use the sensor that the gauge is callibrated to. You can remove the sender for the factory gauge if you're not going to use it, though you'd want to use a sender that you can tap into the factory provisions. I'm pretty sure that there are only a few standards for the sender units, too, so maybe you can find a gauge which will work with the factory sender.