A simplified radiative collapse model has been applied to a high-Z (Ce) lowinductance vacuum spark plasma, in order to assess the possibility of using this simple discharge to generate N-shell atomic quasi-continua for optical pumping of soft x-ray lasers. The radiative losses of the complex Ce ions are computed using statistical methods developed for unresolved transition arrays, and atomic data from the average ion model. The calculations predict that at sufficiently high current, a radiative collapse followed by micropinching takes place at the opening of the M-shell, in good agreement with experimental observations. The model predicts that the radiative losses associated with the quasi-continuum emission allow the plasma to be compressed to relatively high density prior to the micropinch. Nevertheless, despite this 'mild' radiative collapse, the average quasi-continuum brightness is below that required for optical pumping. Scaling the results to discharge currents shows this limitation to be intrinsic to Z-pinch type discharges.