Perhaps.
Levy:
1. To impose or collect (a tax, for example).
2. To draft into military service.
3. To declare and wage (a war).
Under that same loose definition, does not anything that levies war against the United States commit treason? In other words, did Spain commit treason when it levied war against the United States in 1898? If treason is defined as any act of levying war against the United States, it must be true that they did. Yet surely it must be conceded that this position is absurd, as charging another country with treason for simply being engaged in a war with the United States is silly.
That aside, historically the south did not "levy war" against the united states. Rather the northern states levied war against them and, as participants in that war, they defended their territory against an invading army.
Otherwise you have to argue that the Constitution does not mean what it says, but only means it under certain circumstances or conditions.
Not necessarily. As demonstrated above, it is absurd to conclude that by way of the treason clause, the Constitution considered the participant in any type of warfare whatsoever opposite of the United States to be treason within the United States. It is therefore reasonable to assume that the term is legally defined and used by what is most likely a common law tradition. By reading it in that light one may come to Spooner's argument.