Short answer: heck yes. But it depends.
This is one of the internet topics that go round and round with lots of hand waving, but not much to back up opinions. I decided to test it for myself.
Turns out that it's a bad idea if you don't turn off VR with high shutter speeds. You’ll lose about 9% of resolution with your shutter at 1/1000 if you leave vibration reduction (VR) ON. Turn it off if you go above 1/1000! It's lens-dependent in the range between 1/500 and 1/1000. My Sigma 150-600 generally works best with vibration reduction ON between 1/500 and 1/1000.
BUT not all lens VR is created the same. The Sigma 150-600 firmware update 1.01, for instance, seems to have changed this story. VR works with higher shutter speeds in this case. Same goes for the Nikkor 24-70 f/2.8 VR; you can use higher shutter speeds at least with these lenses. Check out the link here for more.
Present technology in vibration reduction can only run up to so high of a frequency, and that limit corresponds to about 1/500 second. Beyond that shutter speed, it actually hurts more than it helps. Below that speed, it can be an amazing aid to keep pictures sharp.
I tried some tests using the Sigma 150-600 Contemporary at 600mm, 1/1000, f/6.3, ISO 2000, using the factory image stabilization (OS) algorithm. I used the 'overall' image stabilization, versus the 'panning' stabilization algorithm, since the viewfinder image showed the subject moving as much vertically as horizontally. The basic idea is the same for Nikkor lenses with "VR", although you don't get as many options for VR algorithms as Sigma provides. I set the lens onto a tripod with a gimbal mount, but I left the gimbal adjustments loose and held onto the Nikon D7100 and used AF-C while I tried to train the focus sensor on the middle of my resolution target at about 55 feet. These are typical shooting conditions, where the subject is jumping around in the frame and you'd swear that VR would be a good idea.
Here's the first set of test results:
VR (OS) ON while shooting the target with AF-C (using back-button focus).
MTF50 Max. MTF50 Min. (corners)
Average maximum resolution = 43 lp/mm
Average minimum resolution = 28.67 lp/mm (corners)
Here's the second set of test results:
VR (OS) OFF while shooting the target with AF-C (using back-button focus).
Average maximum resolution = 46.7 lp/mm
Average minimum resolution = 30.2 lp/mm (corners)
Comparing the two tests:
46.7 / 43 = 1.09 = 9% sharper with VR OFF while using 1/1000 shutter.
30.2 / 28.67 = 1.05 = 5% sharper with VR OFF (corners) using 1/1000 shutter.
Also, notice that the results vary more when using vibration reduction at high shutter speeds.
Therefore, don’t use VR going beyond 1/500 shutter! Unless your own tests of a specific lens indicate otherwise, that is. Life is so complicated.