If your receptacles are not grounded, the plug-in tester may fail to actuate the GFCI. But the GFCI does not require a grounded circuit to function properly in normal use.

Bus is right... the handheld tester leaks a small amount of current from the hot to the ground pin. If the ground pin is not connected that won't trip things. The button on the GFCI just loops a little of the current around the sensing circuitry so it cares not about ground (in fact, there is NO connection to the ground terminal by the GFCI guts at all).

I'm not that big on testing things but I'll often push the button on those and the arc faults if I'm in the panel (or near the receptacle) for some other reason.

I'm also the kind who waits until the smokes start feeping before getting around to replacing the batteries.

The button on the GFCI is the accepted test.