  We revisit the problem of low-mass pre-main-sequence (PMS) stellar evolution
and its observational consequences for where stars fall on the
Hertzsprung-Russell diagram (HRD). In contrast to most previous work, our
models follow stars as they grow from small masses via accretion, and we
perform a systematic study of how the stars' HRD evolution is influenced by
their initial radius, by the radiative properties of the accretion flow, and by
the accretion history, using both simple idealized accretion histories and
histories taken from numerical simulations of star cluster formation. We
compare our numerical results to both non-accreting isochrones and to the
positions of observed stars in the HRD, with a goal of determining whether both
the absolute ages and the age dispersions inferred from non-accreting
isochrones are reliable. We show that non-accreting isochrones can sometimes
overestimate stellar ages for more massive stars (those with effective
temperatures above \sim 3500 K), thereby explaining why non-accreting
isochrones often suggest a systematic age difference between more and less
massive stars in the same cluster. However, we also find the only way to
produce a similar overestimate for the ages of cooler stars is by selecting
parameters that are strongly inconsistent with both theoretical models and
observational constraints. We therefore conclude that inferred ages and age
spreads for cool stars are reliable, at least to the extent that the observed
bolometric luminosities and temperatures are accurate. Finally, we note that
the time-dependence of the mass accretion rate has remarkably little effect on
low-mass stars' evolution on the HRD, and that such time-dependence may be
neglected for all stars except those with effective temperatures above \sim
4000 K.
