Can accelerations be used to calculate load factors?
It sure can; in fact, they are equivalent (with an offset of 1G).

In the body frame, the vertical equation of motion is:

$$Z+mg\cos\theta\cos\phi=m(\dot{w}+pv-qu)$$

Accelerometers can't measure inertial or gravitational forces, so vertical acceleration as measured is $N_z=Z/m$.