Does removing anti-skating really improve sound?

Larry, yes when the groove velocity (modulation) increases friction of the stylus in the groove increases increasing the skating force. Groove velocity also decreases as you move to the center of the record. Now, do you set your tracking force to track light passages allowing mistracking on the heavy ones chewing up the grooves? I think not. Tracking force  is set heavy enough to make it through the tough passages. Same thing goes for antiskating. You are adjusting it to minimize tracking distortion. Cleeds, please excuse me. I should have clarified myself better. I meant tracking distortion. Even order harmonic distortion can be euphoric. Pass intentionally designs a little of it into his amps. Other distortion not so, at least over 1%. Usually the bias adjustment bands are at mid disc. I guess the thought is to get an average velocity.
There are many variables you just can not account for. But, the goal is to minimize miss tracking. Any pivoted arm cartridge combination with properly adjusted anti skate is going to easily out track one without. Get a test record and prove it to yourself. If the stylus leans a little bit to one side or another makes no sonic difference. This is another reason so many of us don’t switch to a tangential tracker. There is no sonic improvement to justify the added complexity. 
Larry, Peter has no idea what the cartridges he is reduilding have been through. The owners usually have no idea.
The primary determinants of the skating force in a given arm cartridge combination are VTF and groove velocity. Modulation is a minor contributor. The geometry of the best anti skating devices is such that the counter force applied decreases automatically at the arm moves towards the center of the record compensating for the decreasing groove velocity.

Since kinetic friction (the force of friction between two moving objects) is only a function of the normal force (the force vector that is perpendicular to the contact surfaces of the two objects) and the coeffecient of friction (mu) between the two objects, stylus velocity should in fact have no effect on the magnitude of the skating force.  So, for a cartridge and an LP, only the vinyl groove, the shape of the stylus, and the VTF should count.  The reason the skating force does change in magnitude across the surface of the LP is due to the ever changing tracking angle error and to groove tortuosity, which forces the stylus to accelerate around the tiny curves in order to hold the speed of its travel constant.  These mini-accelerations of the stylus tip, which are happening at all points, cause mini-changes in the force exerted by the tonearm to hold the cartridge in place and corresponding changes in the skating force. That's the way I see it, given that velocity is not a factor in the formula for kinetic friction.

Actually Lewm groove velocity takes into account the length of the path the stylus travels through the groove. The more tortuous the higher the velocity. The force required to move the stylus back and forth is seen by the system as friction. So, the higher the groove velocity the higher the friction. Groove velocity is not the speed of the record past the stylus. Velocity depends on speed, frequency and modulation. Accordingly, skating force decreases as the arm travels inwards. Most modern anti skate mechanisms compensate for this at least to some degree. Tracking angle error has very little to do with it as long as the arm is set up correctly. It is all about friction and offset angle and offset angle is fixed.

Mijo, No.
I was going to leave it at that, but let me take your statements in reverse order:

"Tracking angle error has very little to do with it as long as the arm is set up correctly. It is all about friction and offset angle and offset angle is fixed."  It's actually about the friction force, we both agree, and about the degree to which the cantilever is not tangent to the groove.  A major reason for lack of tangency, for all tonearms that are mounted such that the stylus overhangs the spindle, is headshell offset angle.  Again, we agree.  But in addition to the headshell offset angle, there is a variable lack of tangency to the groove, created by the tonearm geometry.  At the two null points of any typical alignment algorithm, where the cantilever is tangent to the groove (tracking angle error = 0), there is still a skating force due to headshell offset angle.  But at all other points on the LP surface, headshell offset angle is not the only cause of lack of tangency.  That additional ever changing angle is one reason why the skating force is changing all the time.

"The more tortuous the higher the velocity. The force required to move the stylus back and forth is seen by the system as friction. So, the higher the groove velocity the higher the friction."  That's a very appealing concept, and I was sort of thinking that way too, but "velocity" does not appear in the equation for friction.  So you and I cannot have it that way. The way I see it now, the tortuosity of the groove results in those mini-acceleration events; the stylus MUST obey the speed of the turntable.  No matter how many twists and turns in the groove.  Thus, the stylus is experiencing mini-accelerations (acceleration = change in velocity) as it is dragged around the LP at a constant net speed through those zigs and zags of the groove.  Acceleration does generate a Force.  (Remember, F = ma.)  Those small forces being generated, acting through lack of tangency to the groove wall, must be resisted by the cantilever, the cartridge body, and ultimately the stiff tonearm to which it's attached.  That contributes to the skating force as well.