Depends on Q.

My understanding is that the regulatory behaviour is from saturation (i.e. the core is grossly undersized) and that the extra resonant winding exists just to reduce additional harmonic content, i.e. prevent it producing just square waves. So the quantity of energy stored by the resonant coil would represent probably a cycle or two's worth at nominal load. But it could well be many cycles, depending on the damping factor of that resonant system.