Absolutely. In my experience it's right around 40-45 mph and multiples thereof. And it sometimes has NOTHING to do with the tires. I've experienced this when:
Put a top case on a '90 VFR. Anything over a pound or two in it and got that symptom.
Ventura luggage on multiple VFRs did this IF the case was mounted behind the rear seat. Flip it around so the bag was over the passenger seat and all was stable.
An ST1100 with what turned out to be a bent rear shock rod (new from factory) had this same problem.
Dunlop tires in the early 90's on my VFR did this after a couple thousand miles. They cupped and vibrated and caused the headshake as well. Running them at lower pressure solved the problem but I didn't like the handling.
A Metzler bias ply tire on my '87 VFR did this from new. Took it back and got it rebalanced. Same issue. Finally someone noticed the runout on the tire was out of spec. A new tire fixed the issue. Runout, in this case, was left-right motion of the tire when you spun it on the balancer. It was about 3mm and the maximum spec for it was about half that I think.
Flattened steering head bearings did the same thing. Replacing them fixed it.
There were articles back in the day about loading motorcycles and how any weight behind the rear axle was bad news. This kind of headshake was pointed to as one of the symptoms of an improperly loaded bike. It also had a lot to do with fork flex, tire sidewall flex, frame stiffness, etc. so things might be a bit different now with upsidedown forks, stiffer frames, bigger tires.
The thing that always fascinated me was that one finger on the bars and you never knew the headshake was there. Given total freedom, it shook like crazy.
Hands off the bars on the Ninja causes nary a wiggle. See:
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