The use of gamma-ray burst (GRB) energetics for cosmography has long been advanced as a means to probe out to high redshifts, to the epoch of deceleration. However, although relatively immune to systematic biases from dust extinction, the prompt energy release in GRBs, even when corrected for jetting geometry, is far from being a standard candle. In this work we explore the cosmographic potential of a GRB standard candle based on the newly discovered relation by Ghirlanda and coworkers between the apparent geometry-corrected energies (E$_γ$) and the peak in the rest-frame prompt-burst spectrum (E$_p$). We present an explicit, self- consistent formalism for correcting GRB energies with a thorough accounting for observational uncertainties. In contrast to other work, we demonstrate that the current sample of 19 GRBs is not yet cosmographically competitive with results from Type Ia supernovae (SNe Ia), large-scale structure, and the microwave background. Although the E$_p$-E$_γ$ relation is a highly significant correlation across a range of cosmologies [0<=Ømega$_M$, Ømega$_Łambda$<=2], the goodness of fit of the data to a power law (E$_p$åisebox-0. 5ex E$^η$$_gam ma$) depends strongly on input assumptions. The most important of these assumptions concern the unknown density (and density profile) of the circumburst medium, the efficiency of converting explosion energy to gamma rays, data selection choices for individual bursts (some of which were not included in similar work), and assumptions in the error analysis. Independent of assumptions, with very few low-z bursts, the current sample is most sensitive to Ømega$_M$ but essentially insensitive to Ømega$_Łambda$ (let alone the dark energy equation of state w). The relation clearly represents a significant improvement in the search for an empirical GRB standard candle but is further hindered by an unknown physical basis for the relation, the lack of a low-z training set to calibrate the relation in a cosmology- independent way, and several major potential systematic uncertainties and selection effects. Until these concerns are addressed, a larger sample is acquired, and attempts are made to marginalize or perform Monte Carlo simulations over the unknown density distribution (which itself may evolve with redshift), we urge caution concerning claims of the utility of GRBs for cosmography and especially attempts to combine the results from GRBs with those of SNe Ia.