  Type Ia Supernovae (SNeIa) used as standardizable candles have been
instrumental in the discovery of cosmic acceleration, usually attributed to
some form of dark energy (DE). Recent studies have raised the issue of whether
intrinsic SNeIa luminosities might evolve with redshift. While the evidence for
cosmic acceleration is robust to this possible systematic, the question remains
of how much the latter can affect the inferred properties of the DE component
responsible for cosmic acceleration. This is the question we address in this
work. We use SNeIa distance moduli measurements from the Pantheon and JLA
samples. We consider models where the DE equation of state is a free parameter,
either constant or time-varying, as well as models where DE and dark matter
interact, and finally a model-agnostic parametrization of effects due to
modified gravity (MG). When SNeIa data are combined with Cosmic Microwave
Background (CMB) temperature and polarization anisotropy measurements, we find
strong degeneracies between parameters governing the SNeIa systematics, the DE
parameters, and the Hubble constant $H_0$. These degeneracies significantly
broaden the DE parameter uncertainties, in some cases leading to ${\cal
O}(\sigma)$ shifts in the central values. However, including low-redshift
Baryon Acoustic Oscillation and Cosmic Chronometer measurements, as well as CMB
lensing measurements, considerably improves the previous constraints, and the
only remaining effect of the examined systematic is a $\lesssim 40\%$
broadening of the uncertainties on the DE parameters. The constraints we derive
on the MG parameters are instead basically unaffected by the systematic in
question. We therefore confirm the overall soundness of dark energy properties.
