Is the ADM Mass for a boosted black hole $M$ or $\gamma M$? If you were to take the metric for a Schwarzschild black hole and "boost" it, such that it were traveling with velocity $v$, would the ADM mass, corresponding to a time translation, be $M$ or $\gamma M$, where $\gamma = \tfrac{1}{\sqrt{1 - v^2} }$?
If this were the case, maybe "ADM energy" would be a better name than "ADM mass."
 A: What ADM defined was an energy-momentum vector, which can be interpreted as the energy-momentum vector of an isolated object in the frame of reference of a distant observer. (The notion of a distant observer only makes sense because we assume an asymptotically flat spqcetime.) This energy-momentum vector transforms as you would expect, so yes, the energy component becomes $\gamma M$ if you're not in the rest frame of the object. The ADM mass can be defined as the norm of this four-vector.  For a more detailed discussion of this, see Wald, p. 293. The sentence that explicitly answers your question is the one beginning with "Furthermore, the Einstein evolution equations..."
A: In an asymptotically flat spacetime the ADM energy is formulated as an integral over a two-sphere at spatial infinity. The metric is written as $g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu}$, where $\eta_{\mu \nu}$ is the Minkowski metric and $h_{\mu \nu}$ is assumed to be small at spatial infinity. If $h_{\mu \nu}$ is time-independent at infinity, the ADM energy agrees with the Komar energy (associated to the timelike Killing vector), which in turn matches with a Schwarzschild mass/energy.  
However both Komar and Schwarzschild refer to a massive object at the origin of the coordinates. In your question you think of a boost for the black hole and then you assume the Lorentz factor $\gamma$ of special relativity. As in a curved manifold a global inertial reference frame does not exist, I do not think that your reasoning is applicable.  
Note: In general relativity mass means energy, that is rest mass + kinetic energy + interacting energy of the constituents of an object.
