Yes, one can view self inductance effect as a manifestation of positive electromagnetic mass similar to when accelerating charged sphere by external force, with one important difference: in the case of sphere, the increased apparent mass is due to electric field of the sphere itself. In the case of electrons in inductor, the increased mass is due to field of other electrons in the same inductor.
The applied voltage means there is external impressed force on the electrons in the inductor, but the electrons move as if they had larger rest mass than the standard electron mass. The apparent extra mass is a result of induced electric field of the inductor acting against acceleration of the electrons.
This induced field is directly proportional to acceleration of the electrons with constant of proportion related to inductor's self-inductance L.