  I adopt a formalism previously developed by Catelan and Theuns (CT) in order
to estimate the impact of primordial non-Gaussianity on the quasi-linear spin
growth of cold dark matter protostructures. A variety of bispectrum shapes are
considered, spanning the currently most popular early Universe models for the
occurrence of non-Gaussian density fluctuations. In their original work, CT
considered several other shapes, and suggested that only for one of those does
the impact of non-Gaussianity seem to be perturbatively tractable. For that
model, and on galactic scales, the next-to-linear non-Gaussian contribution to
the angular momentum variance has an upper limit of $\sim 10%$ with respect to
the linear one. I find that all the new models considered in this work can also
be seemingly described via perturbation theory. Considering current bounds on
$f_\mathrm{NL}$ for inflationary non-Gaussianity leads to the quasi-linear
contribution being $\sim 10-20%$ of the linear one. This result motivates the
systematic study of higher-order non-Gaussian corrections, in order to attain a
comprehensive picture of how structure gravitational dynamics descends from the
physics of the primordial Universe.
