How feasible is it to join the National Guard and serve while in graduate school to pursue an MBA?

There are folks in the Guard working on their MS, MBA, PhD, JD, PA school, etc.
It all depends on your ability to balance your civilian career, family, and Guard requirements.
Bear in mind, you may need to attend a school to become branch qualified in the Guard.

Yes, a lot of soldiers continue their education while serving in the National Guard, and as SFC Boyd has pointed out, a number of states offer some very substantial educational benefits beyond GI Bill. To continue from your other thread, I am assuming that the Guard accepted your current Branch and that you are a fully qualified 1Lt. When I branch transferred to the Engineers when I went to the Kentucky Guard, I did have a time limitations on Branch Qualifying, but by completing what is now the Captains Career Course. That is available as a three phase course, 2-14 day segments (phase 1 and phase 3, phase 2 is distance learning, but you will have to work that in to stay qualified.

There are plenty of grad students on the O and E side of the fense serving in the reserves and guard. Especially now with online learning being so accessible