Does removing anti-skating really improve sound?

Trusting your ears and knowing what you like to listen to are two very different subjects. Distinguishing fine differences in sound is difficult for humans because our audio memory is so short. Not only this but because of our brains ability to accommodate a system that sounds awful does not sound so bad after a while which is why you always trust your initial impression. Fortunately distortion being so dissonant is always easy to hear like the elephant in your garage is easy to see. Knowing these things makes you a much better listener. Most of what Cleeds thinks he hears is his brain screwing around with him assuming he has one. 
Any pivoted offset tonearm that does not have anti skating can be thrown in the trash unless you want to jury rig a system for it. Turntable setup is not art, it is a science requiring extreme fastidiousness. There are lots of things brains can't do well which is why we have test records.
Raulruegas the best you can do is to set the bias so the stylus tracks the test record correctly. It is the best approximation you can get. Looking at the cantilever only gets you in the ballpark. This method will not work with very stiff cartridges like Koetsus. The other neat trick is to find an album with a blank side like Cleopatra by the Lumineers. You can get in the ballpark by adjusting the bias so the arm does not drift or drifts outward slightly when you play the blank. Never trust the scales on the tonearm. They are great for reference. For example if you are a cartridge jockey you record all the settings for each cartridge so you can return to them easily without having to go through the whole process again. 

rauliruegas

Yes but the problem word in that statement is: " correctly " and till today exist no single method/mechanism to set up " correctly ".

That's really not quite true. Just because something can't be executed perfectly doesn't mean that it can't be done; there's no reason to let perfection be the enemy of the good. In engineering, everything has a tolerance, and the same is true of anti-skate. There's no reason not to use anti-skate just because you aren't certain that a given setting is "perfect."

There is a huge difference between evaluating a change in sound quality and knowing what you like to hear.  We have a notoriously short audio memory and if we listen to a system that sounds "bad" long enough after a while it does not sound as bad. This is why you always trust your first impression. Fortunately distortion is easy to hear because it is so dissonant, sort of like looking for an elephant in a garage full of cars.
Rouliruegas, the best you can do is setting the bias with a test record. That is what I mean by correctly and yes it is not perfect. It can't be. there are too many changing variables you can not correct for. Viewing the cantilever angle just gets you in the ballpark and even that does not work well with very stiff cartridges like the Koetsu. Another neat trick to get you in the ball park is using a blank record. Cleopatra by the Lumineers is a three sided disk. The forth side is blank. You adjust the bias until the arm starts to drift backwards playing the blank side then fine tune with the test record. 
Any arm without bias adjustment is trash unless you want to jury rig a bias mechanism for it. The primary problem is not sound quality or wear. It is tracking distortion. Any arm without bias is going to miss track the outside groove wall at lower velocities than a properly set up arm. Any good test record will demonstrate that. They are relatively cheap. Don't listen to me. Prove it to yourself. Oh, do not trust the gradations on the tonearms. They are good for reference. Cartridge jockeys can write down the settings so that when they change cartridges they can go back to the proper setting without having to go through the whole routine again. 
Creed,  I am an MD and can guarantee you I know a lot more about the brain than you do. You are not your brain. You as a psychological entity are a maze of bioelectrical reactions taking place in what is hopefully a brain. Soon it might be in a computer. I can damage your brain and disrupt those reactions and you won't be there any more but the brain still is. Alzheimers disease is a way of doing it slowly. Now, where you go afterwards is a matter of debate. Audio sales people are generally headed south.  

Larryi you are essentially correct except for one thing. It is the loudest passages you want to set the tonearm for as they are the hardest to track. The lighter passages are easy and a little more bias here does not matter near as much. It is the stylus following the groove that you are interested in nothing else. Fidelity will not change at all until the cantilever is way off center in the non linear zone. Very stiff cartridges, very low compliance like the Air Tight and Koetsu might sound just fine playing a string quartet without anti skate. Put on Aerosmith and they will pop right out of the groove.  
All this is the argument for tangential tonearms. I have had three of them and can guarantee they are way more headache and unreliable than a good pivoted arm. Just ask Michael Fremer.  

I use a linear tracker (Kuzma Airline) and the fine horizontal balancing set up involves bouncing the arm while it is in its 'up' cueing position at different points along the face of a record to see which way the arm drifts-- the objective, if I recall the instructions correctly (and I re-read them when I do this setting) is drift slightly outward at rim of record, neutral at center of record and slightly inward an inner grooves. This is supposed to be more exact than any level or measure and in fact that has proven true. So the arm is level, but....
I haven't used a conventional arm for a dozen years but am adding one- it's en route to me now, and it has an anti-skate device. So, I will be doing his setting for the first time in a long time.
Riddle me this- using a test record, are you checking for anti-skate at more than one place on the record? If not, why not? (Not a trick question and no hidden agenda other than my curiosity and fairly long lack of hands on experience in messing with an anti-skate setting).