Kalman Filter for position : introducing acceleration estimates
If the acceleration readings are performed in an inertial (non rotating in particular) frame then yes it's sufficient to use the accelerations, but if the acceleration measurements are performed on the moving craft then no it's not possible alone by accelerometer readings. 

Eventhough it's sufficient to use those accelerations $a_x$, $a_y$, and $a_z$ on a cartesian coordinate system to compute the displacement associated with the center of mass of the craft that's moving in 3D, nevertheless you will also need to know the orientation of the craft (hence the accelerometer) so that you can transform its acc measurement vectors into the navigation frame correctly. 

Therefore, you also need to consider (at least) the gyroscopic readings to determine the craft orientation wrt your navigation frame. Once you determine the orienation of the craft, then you convert its current acceleration measurements into the non-rotating intertial frame in which you compute the track of the craft by integrating the accelerometer readings.