No, the 'Speed Wobble' is more to do with resonant frequency and if you try to control it through steering it gets worse

Also the more stiff a frame is then the more susceptible it can be to doing it, my 531c Road Ace can be a beggar for it and conversely slackening the 'death grip' on the handlebars normally cures it on that as does laying one leg against the top tube.
I think it is a valid link and connection to make.
The speed wobble resonance appears to be a circular steering reaction that cannot be arrested because the system's resonance bounces the action back and forth. Resonance is difficult to pinpoint and predict because of so many contributing factors, but I got lucky, I think.
I've had a bike that always shimmied at 46kph. I had a route with a long downhill of a gradient perfect for allowing me to approach the shimmy point relatively slowly. I could predict the onset and control it by either slowing down (but to a point way beyond it's initial start point) or by destroying the resonance's node. This node seems to be the seat and by standing up I could instantly arrest the shimmy. I got very good at it and eventually could do it no-hands and no-hands standing up. In the latter position I had to clamp the seat between my thighs and for those interested, it did not stop the shimmy. My theory is that it didn't destroy the node.
By the time I moved away from the area I must have repeated the exercise 30 or 40 times. My mates got bored with my tricks and musings and bored with having to wait for me at the bottom of a very, very long gradient that just asked for free speed.
I got double lucky in my amateur analysis of the problem. I had a Cannondale CAAD4 at the time. However, I had an exact geometric replica of that bike made from steel. The reason for that was that I wanted to build my own bike after I purchased a jig from a framebuilder who went out of business. I ordered a set of tubes from Ceeway and because I had no experience with designing frames, I simply copied my Cannondale's angles and tube lengths.
The equipment on both bikes weren't exactly the same though. The one had 28-spoke wheels, the other 32. The groupset was also from different eras albeit the same brand and level. Stem and handlebars were dimensionally the same but brandwise not.
Only the steel bike shimmied at that speed. I never managed to find a speed at which the Cannondale would shimmy although, of course, given the right conditions and load it would shimmy somewhere this side of the speed of sound (my maximum on a good day).
Although it is extremely difficult to really say, I could swear that I could see the stem swivel left and right, exactly like counter steering. Hence my theory of counter-steer bouncing backwards and forwards within the frame's boundaries of flexibility.