In my head an ab initio model is one that comes from first principles and is as basic as you can get.
Since Classical EM is just a low velocity, course grained approximation for Quantum ElectroDynamics (QED), it is not from first principles.

However this is a purely elitist argument as a physicist. If a Material Engineer uses Classical EM and calls it ab initio I would be much happier than when they used a phenomenological model and correctly labelled it as such.