If you are going tubeless to take advantage of the lower pressures, then yes, you will definitely see noticeable improvements. I did.
If you are not getting flats with your current pressures with tubes, there is no reason not to run them that low. But with tubeless you will be able to go lower.
Smaller tires like you have and are considering (2.0-2.2) in my experience get the most benefit of all from running tubeless, because with smaller tires it is usually pinch flats that limit how low you can go with tire pressure.