The "smoking gun" of small-scale, impulsive events heating the solar corona is expected to be the presence of hot (>5 MK) plasma. Evidence for this has been scarce, but has gradually begun to accumulate due to recent studies designed to constrain the high-temperature part of the emission measure distribution. However, the detected hot component is often weaker than models predict and this is due in part to the common modeling assumption that the ionization balance remains in equilibrium. The launch of the latest generation of space-based observing instrumentation on board Hinode and the Solar Dynamics Observatory (SDO) has brought the matter of the ionization state of the plasma firmly to the forefront. It is timely to consider exactly what emission current instruments would detect when observing a corona heated impulsively on small scales by nanoflares. Only after we understand the full effects of nonequilibrium ionization can we draw meaningful conclusions about the plasma that is (or is not) present. We have therefore performed a series of hydrodynamic simulations for a variety of different nanoflare properties and initial conditions. Our study has led to several key conclusions. (1) Deviations from equilibrium are greatest for short-duration nanoflares at low initial coronal densities. (2) Hot emission lines are the most affected and are suppressed sometimes to the point of being invisible. (3) For the many scenarios we have considered, the emission detected in several of the SDO-AIA channels (131, 193, and 211 Å) would be dominated by warm, overdense, cooling plasma. (4) It is difficult not to create coronal loops that emit strongly at 1.5 MK and in the range 2-6 MK, which are the most commonly observed kind, for a broad range of nanoflare scenarios. (5) The Fe XV (284.16 Å) emission in most of our models is about 10 times brighter than the Ca XVII (192.82 Å) emission, consistent with observations. Our overarching conclusion is that small-scale, impulsive heating inducing a nonequilibrium ionization state leads to predictions for observable quantities that are entirely consistent with what is actually observed.