We analyze deep X-ray, optical, and mid-infrared Spitzer observations of the CDF-N/GOODS-N region to study a sample of 13 submillimeter-detected galaxies with spectroscopic redshifts (median z = 2.2). These galaxies are among the most active and massive at this epoch. We find evidence for a power-law correlation between the estimated stellar and X-ray luminosity, implying that masses of the black holes may be related to the stellar masses of their host galaxies. We derive the rest-frame UV-near-infrared spectral energy distributions for these galaxies, believed to be young spheroids, and fit them with model templates. Using the rest-frame near-infrared luminosities, which are relatively insensitive to uncertainties in stellar ages and reddening in these young dusty galaxies, and theoretical mass-to-light ratios, we can estimate their stellar masses. Although the submillimeter emission implies that these galaxies are undergoing an epoch of intense star formation, the Spitzer data reveal a massive stellar population already in place. We find that our submillimeter galaxies have a median stellar mass of ~10¹¹ M, which is roughly 10 times more massive than typical UV-selected star-forming systems at similar redshifts. These stellar masses are then compared to previously published black hole mass estimates derived from the X-ray luminosities under the assumption of Eddington-limit accretion. We find that the black hole masses for our high-redshift sample are approximately 1-2 orders of magnitude smaller than galaxies of comparable stellar mass in the local universe. Although our estimates of black hole masses will increase if the accretion is sub-Eddington, and our stellar masses will decrease if we assume a much younger stellar population or a different initial mass function, we find that only through a combination of effects is it possible to shift the high-redshift galaxies such that they lie on the local relation. This suggests that the black holes need to grow substantially between z = 2.2 and the present day, with much of the black hole growth occurring after the current obscured, far-infrared luminous phase of activity, which is likely associated with the formation of the spheroid. This interpretation supports a scenario in which submillimeter galaxies pass through a subsequent accretion-dominated phase, where they would appear as optically bright quasars.