  In previous work, two of us have proposed a model of inflationary
magnetogenesis based on a rolling auxiliary field able both to account for the
magnetic fields inferred by the (non) observation of gamma-rays from blazars,
and to start the galactic dynamo, without incurring in any strong coupling or
strong backreaction regime. Here we evaluate the correction to the scalar
spectrum and bispectrum with respect to single-field slow-roll inflation
generated in that scenario. The strongest constraints on the model originate
from the non-observation of a scalar bispectrum. Nevertheless, even when those
constraints are taken into consideration, the scenario can successfully account
for the observed magnetic fields as long as the energy scale of inflation is
smaller than $10^6\div10^8$~GeV, under some conditions on the slow roll of the
auxiliary scalar field.
