Does removing anti-skating really improve sound?

it depends on the stylus tip profile, it’s better to use antiskating if you don’t want to destroy one side of the vinyl groove wall

and tilt the cantilever inexorably from one side :(

Only for cartridges that require a high reading loss 2.5 -3gr. and superior the antiskating loses effectiveness.

There are exactly two reasons why tonearms skate. The offset angle of the tonearm and friction of the stylus in the groove. The tonearm is being pulled towards the spindle leaving the stylus and cantilever behind forcing the cantilever's suspension into a non linear zone like trying to run a woofer pinned against the end of its excursion. What this effects most is the cartridges tracking ability. You can prove this to yourself with any good test record like the Hi-Fi News Analogue Test LP. Play the Bias Setting band and lift your anti skate weight. The left channel will start buzzing madly. Add a lot more weight and the right channel will start buzzing madly. Get it right and both channels play the test tones beautifully. This is the only right way to set anti skate and it is at best an approximation as the skating force changes with groove speed and degree of modulation. Any setup that sounds better without anti skating was not set up correctly to begin with. 
Tangential tonearms that are set up correctly do not skate because they are dead straight. There is no force vector off the main axis of the tonearm. Their main theoretical advantage is that they don't skate, improving tracking no matter the  speed of the groove or modulation. There is no audible benefit in them being perfectly tangent to the groove at all times and they have one major failing which is the effective mass in the horizontal plane is way higher than the vertical plane leading to two separate resonance points and stress on the cantilever moving that huge horizontal mass. Watch any of these arms with a reasonably compliant cartridge like the Ortofon Windfeld Ti and what you will see is the cantilever drift towards the record center and the the tonearm catching up to it in a cyclical manner. The benefits simply do not out weight the compromises which is why most vinylholics won't use them. I can make any of the better Rega or Project arms sound better than any straight line tracker. We are in the golden age of the turntable now. There are some fantastic inexpensive complete turntables out there. As long as you have them set up on a rock solid surface and the tonearm is set up right you will not be able to do better without spending stupid serious money. 
Final trick of the day. If you want to get your azimuth dead on just get a thin pocket mirror and place it on your platter. Lower the stylus on it.  Light up the stylus with a spot light and you will see the stylus and its reflection make an "hourglass." Adjust your arm until the hourglass is perfectly symmetrical.
This more than doubles your accuracy.

You can prove this to yourself with any good test record like the Hi-Fi News Analogue Test LP. Play the Bias Setting band and lift your anti skate weight. The left channel will start buzzing madly. Add a lot more weight and the right channel will start buzzing madly. Get it right and both channels play the test tones beautifully. This is the only right way to set anti skate and it is at best an approximation as the skating force changes with groove speed and degree of modulation. Any setup that sounds better without anti skating was not set up correctly to begin with.

I'm glad someone else has mentioned Hi-Fi Test LP finally. 
Because people normally posted something like "adjust by ear or using CD or blank record" 

Hi-Fi Test LP is a must have, not only for anti-skating, but for eoverall setup, there is a free protractor inside. 

Why don't readers here just remove then restore a/s to hear if you like it or not

Stringreen, the most important thing I have learned in this passionate hobby over the last 55 years is, Never Trust Your Ears. The problem with ears is that they are connected to a brain. Brains can accommodate to stimuli in amazing ways. Example. You walk into a room with a really bad odor. In about 5 minutes you notice it is not near as bad but then another person walks in wrinkles their nose and says "boy it stinks in here!" 
Always follow the science when you have it. Cartridges in pivoted tonearms track much better and have much lower distortion with anti  skating set correctly. Setting up a turntable correctly is not easy. Very few dealers have someone who knows what they are doing. I hate to say this because as a company McIntosh's customer service has no equal but I just had to re adjust one of their MT5 turntables. Not only was it out of alignment but the resonant frequency was too high. I had to add 2 grams of lead to get it down to 10 Hz. It was supposed to have been set up at the factory. 
Every vinyl jockey should have the tools and learn how to do this to get the best out of their turntable. These are, A protractor ( I like the DB Systems best), a pocket mirror, a bright light, a little engineers square, little screwdrivers, cartridge weights, a level bubble and a good test record like the Hi-Fi News Analogue Test LP.