Based on the variety of tasks that are performed in a simulator that VR would have great trouble accurately replicating, I think the answer is likely, no. There IS a role for "simulators" that are more accurately referred to as "procedures trainers" in that they are non-motion, but this has nothing to do with VR, as those don't use all that much visual display anyway. Networked wargaming is a great capability that VR can add to military simulations, but that's an addition to, not a replacement of, traditional simulators.
In a full-motion simulator, there are several things about the simulator that contribute to aircrew training, and the visuals are one important part. The replication of the entire cockpit, including every switch, lever, display, keypad, and so on is another. When I go to the sim and practice emergency procedures, each control reacts exactly as it does in the aircraft: where I look and where I reach to put my eyes and then my hand on each control, how hard I need to pull to get the desired effect, and so on. And where I'm reaching with my sitting height and arm's reach is ever so slightly different than another pilot does. We both get the same control, but it's farther below a tall pilot's eye line than a short pilot's. (Slightly over-simplified, but the basic point remains.)
We also do a fair amount of manipulation of the Flight Management Computer while in the simulator, which involves typing. Not to say that typing isn't possible in VR, but it's not exactly the same as typing on a physical keyboard. And we're using the same physical checklists and iPad EFB's that we do in the aircraft; not sure how well VR can mimic those.
So when you consider all the parts & pieces that make up the modern simulator & its considerable cost, the physical replication of the cockpit probably isn't something you're going to be able to remove in favor of VR.
For basic flying training, some of these sorts of factors are less important, as the basic flying skills you learn on one trainer transfer quite well to another trainer, even with a different cockpit layout. But for basic flying training, not only the visual but also the vestibular and "seat of the pants" elements are more important. While VR goggles like Occulus Rift are probably cheaper than several large display panels for providing the out-the-window visuals, these days high quality visual displays aren't the most expensive part of most simulators, and VR can't simulate the seat-of-the-pants sensation of accelerating, stopping, turbulence, and the like without some sort of motion actuators -- hydraulic or electric.
Now, for networked purposes (i.e. wargaming where Air Force elements from multiple bases across the country or globe can participate without the time & expense of getting to, say, Nellis AFB for a Red Flag), VR has amazing potential. But to the extent that each pilot still has his own realistic cockpit & switches, what's driving the big gains is more the network than the VR... you can network an existing visual display with about the same hardware as you'd network the Rift devices. To the extent that the "reality" of the precise cockpit can be sacrificed, then the VR probably makes for fabulous gains -- units practicing their tactics, rather than precise switchology. Sometimes that's a perfectly acceptable tradeoff; other times, not so much.
But until the tactile feedback of VR is good enough that I can use it to practice putting my hand on a lever, pulling it out of its detent in "this" direction with "this much" force required for "this much" travel, then pushing it down "this far" with "this much" force until it hits the stop "here," I really doubt that VR will replace the high-dollar flight simulators used in military and airline training.