No question about that.
I would argue, though, that the seeds of centralization were planted long before when President Washington sided with Hamilton in his argument with Jefferson about the propriety of a national bank. Chief Justice Marshall then reiterated the same arguments.
Since then, the United States government has grown more or less as fast as Congress has wished. The Civil War just provided Congress with another dragon to slay and another reason for rapid growth.
I'm not so sure that the long-term results are going to be positive, though.
In the last analysis, we the people have to decide how big a government we want. If we ever really want to, we can reduce the size of the federal government.