  We present HST WFC3 F160W imaging and infrared spectral energy distributions
for twelve extremely luminous, obscured AGN at $1.8<z<2.7$, selected via "Hot,
Dust Obscured" mid-infrared colors. Their infrared luminosities span
$2-15\times10^{13}$L$_{\odot}$, making them among the most luminous objects in
the Universe at $z\sim2$. In all cases the infrared emission is consistent with
arising at least in most part from AGN activity. The AGN fractional
luminosities are higher than those in either sub-millimeter galaxies, or AGN
selected via other mid-infrared criteria. Adopting the $G$, M$_{20}$ and $A$
morphological parameters, together with traditional classification boundaries,
infers that three quarters of the sample as mergers. Our sample do not,
however, show any correlation between the considered morphological parameters
and either infrared luminosity or AGN fractional luminosity. Moreover, their
asymmetries and effective radii are distributed identically to those of massive
galaxies at $z\sim2$. We conclude that our sample is not preferentially
associated with mergers, though a significant merger fraction is still
plausible. Instead, we propose that our sample are examples of the massive
galaxy population at $z\sim2$ that harbor a briefly luminous, "flickering" AGN,
and in which the $G$ and M$_{20}$ values have been perturbed, due to either the
AGN, and/or the earliest formation stages of a bulge in an inside-out manner.
Furthermore, we find that the mass assembly of the central black holes in our
sample leads the mass assembly of any bulge component. Finally, we speculate
that our sample represent a small fraction of the immediate antecedents of
compact star-forming galaxies at $z\sim2$.
