  Many binary companions to the central stars of planetary nebulae (PNe) are
found to be inflated, perhaps indicating that accretion onto the central star
might occur during the PN phase. The discovery of a handful of nova eruptions
and supersoft X-ray sources inside PNe supports this hypothesis. In this paper,
we investigate the impact that hosting a steadily-accreting WD would have on
the properties and evolution of a PN. By pairing the published accreting
nuclear-burning WD models with radiation transfer simulations, we extract the
time evolution of the emission line spectra and ionization properties of a PN
that surrounds a 0.6$\rm M_{\odot}$ steadily nuclear-burning WD as a function
of the mass accretion rate. We find that accreting WDs are able to form very
extended, high excitation, [O III]-bright PNe, which are characterised by high
nebular electron temperatures. Their properties remain almost invariant with
time and their visibility time can be much longer compared to PNe powered by
single WDs. We discuss the implications of our findings in explaining specific
characteristics observed in PNe. Finally, we examine how accreting WDs affect
the planetary nebula luminosity function (PNLF) by covering WD masses in the
range of 0.5-0.8$\rm M_{\odot}$ and for various accretion rates within the
steady accretion regime. We find that for all but the lowest accretion rates,
the [O III]-luminosities are almost constant and clustered very close to the
PNLF cut-off value. Our results suggest that mass-accreting WDs in interacting
binaries might play a role in understanding the invariant cut-off of the PNLF.
