Mark,

The test button on the GFI itself tests the electronics and trip circuitry just as effectively as applying an external hot to ground connection.

All the test button does is unbalanced the hot & neutral currents through the sensing xfmr by connecting load-side hot to line-side neutral via a suitable resistance.

About the only way that you could have the test button trip the GFI while a 6mA external fault would not, would be if the test resistor went low in value and at the same time the GFI lost sensitivity. Not likely!