I think that, for the most part, it would so long as laws were written in such a way as to allow for some regional variation. I think that it would work fine but that people would never accept it.
The US is no longer made up of states that differ all that much from one another. Of course, there are differences between California and Texas, for example, but our culture has become so homogeneous that the differences are not so great as they once were.
A unitary government can work in any country where the regions do not have fundamental differences. I think that we no longer have fundamental differences between regions.
As long as the laws were written well enough (to take into account, for example, the different costs of living in Wyoming and New York) there would not be a problem. We Americans are much more like one another now than we were when the Constitution was written.