The role of GPS in INS/GPS navigation systems
By itself, no, it cannot.

Your method of fixing the INS system is pretty clever, but it only accounts for drift in the gyroscope. Accelerometers are also (very) prone to drift, generally showing up as an increasing velocity bias. The typical method to account for accelerometer drift is to use zero-velocity updates. By detecting points when you are not moving, you can periodically remove any non-zero velocities from your model.