And then only when the feds let the state borrow it. Various court cases have determined that a governor has no power over his state's National Guard, if the feds want to use it for something. All guardsmen, and I was one long ago and in far away land (called Oklahoma), are also dual hatted as members of the federal military reserve. Those officers that are to be appointed by the governor according to the Constitution are mostly, but not entirely, people commissioned into the federal military, or in most cases into the federal reserves (ie. ROTC grads, OTC/OCS graduates, or even Academy grads). Those few actually appointed by the states still have to be "federally recognized", which means that the feds could not recognize them, and thus have a veto over what is a power of the states as defined by the US Constitution.
So it's something of a legal fiction that the National Guard is even a part of the State Militia.
That's not true of the State Guard, which is a true militia (although most of the officers are still former federal military officers (but then again George Washington was once an officer in the British Royal Militia). But even the State Guard is not "The" State militia or "the Militia" it's only part of it.
It's especially fiction considering that the feds provide 95% of the funding for the various state National Guards.