"Did the Wii influence modern VR?"

imo not at all.

Did the virtual boy actually have any "real" VR games?
You know first person, you turn your head, the character looks around inside the world? (up,down,around,ect)

Because my impression of the Virtual Boy is it isnt actually a real VR machine.
Its just a flashy branding name (for something it doesnt really do).

Wii was a important stepping stone for VR controllers, I don't think VR developers ignored the Wii motion plus in their pursuit of the ideal VR controller 

A lot of things influenced modern VR. A lot of things have a minor influence on a lot of other things. That's kind of how technology works.

Did the Wii controller influence modern VR controllers? Probably, somewhat. Would it have happened anyway even without the Wii controller? Almost certainly. Technological convergence.

Short answer: No.

Long answer: Hahahaha noooooooooooooooooooo xD

I remember when Nintendo invented the vagina. So good.

I disagree , but if in OP you say that VR boy the one which inspired, maybe there still be a good loong discussion. But this thread is focusing on how Wii mote affecting VR tech side. So the answer is No. Also you need to remember VR is not just PSVR, if you just look PSVR is the only VR then you are greatly mistaken.

I believe the reason you having this idea because PSVR are using Playstation move as tracking device and PS move were inspired by Wiimote, PSVR was inspired by PS moves , that's is the real stories. And PS Moves was indeed inspired by Wiimotes but than again Wii mote laso inspired by Eye Toy. So that's how innovation works.

Also there are a lot of others tracking device for VR device and that is not mimicking/using traditional PS moves/wii remotes. And the discussion will be even longer if you see from the aspect of optical and head set side. How 3D screens also involve on inspiring VR head set etc.

So the answer is "NO"

I watched an episode of Darkwing Duck back in the 90s. His daughter was playing a VR game and she wore a headset, "power gloves" and "power boots". I'd say modern VR is more like that than anything else.

While I agree that VR includes much more than motion controls, I think you make a false point about the timing. If X is inspired by Y to do something new, it often still takes X many years to accomplish it. In that sense it is no surprise, I that motion inputs and gyro headsets in VR came years after the motion control thing died. It is the other way around: if something like this came only a year or two after the Wii, I would say it is NOT inspired by Wii, as development of these things take years and it therefore had to be in development already. Only a more carbon copy thing with slight improvements, like the PS move controller, can be developed so fast. That by the way also means I don't think Kinect was inspired by the Wii, as it is certainly from the basics a different idea. Microsoft only took game implementations in the direction of the Wii motion games, as they saw the success of the Wii-

I m pretty sure if tech for hardware tracking was cheaper at the time of PS2 Eyetoy, it would have been implemented Wii saw the opportunity to implement hardware based tracking an improvement over visual tracking of Eyetoy they went with it, Sony saw that tracking could be further enhanced by implementing both Hardware and visual markers, its called evolution of tech.

So No Nintendo did not invent or introduced tracking in games, even before wii I had a samsung phone on which i used to play motion bowling

I wouldn't give them credit for the design. 

I'd give them credit for mainstreaming motion controls but by the time VR came out it wasn't mainstream anymore we'd mostly moved on. Only the Move seems to take clear inspiration from Wii controllers as especially the oculus rift is very different. It's difficult to be like 'well there Nintendo goes again changing the industry' when it's kind of like giving the tyre manufacturers a shit tonne of credit for the innovation in a Tesla vehicle.