  The properties of unresolved protostars and their local environment are
frequently inferred from spectral energy distributions (SEDs) using radiative
transfer modeling. We perform synthetic observations of realistic star
formation simulations to evaluate the accuracy of properties inferred from
fitting model SEDs to observations. We use ORION, an adaptive mesh refinement
(AMR) three-dimensional gravito-radiation-hydrodynamics code, to simulate
low-mass star formation in a turbulent molecular cloud including the effects of
protostellar outflows. To obtain the dust temperature distribution and SEDs of
the forming protostars, we post-process the simulations using HYPERION, a
state-of-the-art Monte-Carlo radiative transfer code. We find that the ORION
and HYPERION dust temperatures typically agree within a factor of two. We
compare synthetic SEDs of embedded protostars for a range of evolutionary
times, simulation resolutions, aperture sizes, and viewing angles. We
demonstrate that complex, asymmetric gas morphology leads to a variety of
classifications for individual objects as a function of viewing angle. We
derive best-fit source parameters for each SED through comparison with a
pre-computed grid of radiative transfer models. While the SED models correctly
identify the evolutionary stage of the synthetic sources as embedded
protostars, we show that the disk and stellar parameters can be very discrepant
from the simulated values. Parameters such as the stellar accretion rate,
stellar mass, and disk mass show better agreement, but can still deviate
significantly, and the agreement may in some cases be artificially good due to
the limited range of parameters in the set of model SEDs. Lack of correlation
between the model and simulation properties in many individual instances
cautions against over-interpreting properties inferred from SEDs for unresolved
protostellar sources. (Abridged)
