Nope. I suspect the name "Ground Fault Circuit Interrupter" is because this device does not DETECT a Ground Fault; it compensates for a faulty Ground by using a different technique.
In a "normal' circuit with a Ground, the outer chassis of the device you have plugged in is connected to a true Ground via a bare wire in the power cable, all the way back to the breaker panel where it is connected to a true earth Ground. The Ground lead is supposed to carry NO current under normal circumstances so it's at zero volts, and it is just as heavy as the current-carrying Hot and Neutral wires in the cable. So if ever there is a fault in the user device that allows current from the Hot side to leak into an exterior surface that could be touched by people, that current will flow through the Ground lead to earth. This has two important consequences: the current flows easily to Ground so that the voltage at the external surface of the user device is still VERY close to zero and unlikely to cause damage to the person; and, the current flowing in this manner is VERY likely to be so heavy that it will overload the breaker for this circuit at the panel, cutting off power to the Hot lead in a very short time, and thus eliminating the hazard.
BUT, what would happen if the Ground lead were faulty - broken, or badly connected with high resistance to true Ground? The leaking current might not be enough to trip the breaker, and the device surface voltage might be high enough to cause real injury.
A GFCI unit does its job differently. It constantly measures the current flowing in both the Hot and Neutral leads and compares. In a properly-operating circuit, these MUST be equal. If they are not - I believe the tolerance for "not equal" is 5 mA at max, which is not enough to cause disruption to heart muscles when run through a chest - the unit shuts off the connections from the source wires (from the breaker panel cable) to its output connections, thus stopping all current flow. This action does NOT need a Ground lead to function at all. So, if the Ground lead has failed, it still works. In older homes that never had grounded cabling to wall outlets, some electrical authorities accept using a GFCI instead of grounded wiring because it can protect people from stray current flows going to the wrong place. BUT without a real and well-connected Ground lead, a GFIC cannot provide some of the other uses of a true earth Ground. Like, for example, a place to "get rid" of electrical noise signals generated in the outer and inner chassis metal of many devices.
Many jurisdictions mandate having GFCI devices protecting circuits into areas that use water a lot, like kitchens and bathrooms. The idea is that in normal daily use it is possible that water might enter one of the user's plugged-in devices and cause a current leakage path to develop either to the device's exterior, or to a surrounding surface like a counter top or floor. In some such cases the current flow to Ground might be sufficient to cause a breaker trip, but might not. On the other hand, such a leakage path definitely would cause the current flows in Hot and Neutral lines of the power supply to become different (by the amount of leakage current, no matter where it is going) and a GFCI would shut the circuit off to protect people.