It’s really hard to say. With the Magicsee M1/M1 Pro it gives a pseudo head movement effect with the hdmi input as gen1 headsets produce a more pan & scan size picture. Interestly the Magicsee m1 uses head movement to let you see the missing left & right parts of the image.
The biggest problem wiith trying to get VR on a console is whether or not the game supports native vr(psvr) or has something to convert it to VR (Vorpx).
Now if a Video headset supports 3D a game with 3D support on a console might work or if it can upconvert to 3d output.via maybe a device.
But unless your willing to experiment with spending cash on a chance it will work. It would likely be better to wait for a confirmed method that works.
I have never explored it (no xb1 or ps4) I have heard you can do some kind of VR by streaming Xb1 to pc as @g-coded was mentioning.
As for console direct? Not sure perhaps with emulation dongles or special devices to map controller functions might work. The Tilt device 4 example if can work. You might be able to map it like mouse look.(look stick).
Essentially you’d likely need to develope something or have disposable income to experiment.