Yes, it does hold. Mass-energy is the typical term used when talking to laypeople, but physicists tend to use natural units (\hbar=c=k_{B}=eV=1) which means that mass and energy are equal, not just equivalent. E=m, instead of E=mc^2, since c=1. (E^2 =m^2 c^4 +p^2 c^2 becomes E^2 =m^2 +p^2 for high velocities, for the pedantic.) So the terms are interchangeable, as long as you're using the right system of units.
The actual theory (the Alcubierre metric) is a solution to the Einstein Field Equations (the complex system of nonlinear partial differential equations that make up general relativity). However, since these are differential equations they can have many solutions, and indeed many different solutions have been found. It is not known which solution (if any) is correct for the real world. In general, it can't be known for certain until a full theory of quantum gravity is discovered. Indeed, the existence of "Dark Energy" is one of the indications that the theory is slightly wrong. It may be explainable as a modification of the theory or may actually be some sort of negative mass-energy, but at the moment we have no way to tell. Again, we need a complete theory of quantum gravity.
For anyone actually wanting to learn about this sort of thing in detail, try the following, in order:
http://www.amazon.com/Gravity-Post-Newtonian-Relativistic-Eric-Poisson/dp/1107032865 http://www.amazon.com/Gravitation-Physics-Charles-W-Misner/dp/0716703440/
Both are graduate level texts (it's a graduate level theory) and require a thorough understanding of differential equations. And differential geometry, and all the more basic physics on which they build of course. The first book starts with some very good material on Newtonian gravity, but you'll still want to have had at least a year of undergraduate physics to start. The theory is simple, but the solutions are very complicated.