It's important to play with sound, however music can sometimes be distracting.
The statement of the reddit post that says you can hear an enemy recalling is correct, also that you hear certain abilities but the most important thing: You can hear Skillshots hitting enemies in a bush.
Take Morganas Q for example. The skillshot has no graphical indication on whether an enemy is hit or not (only the range) especially if you hit them at max-range. It does however has a sound indicator. So basically if you have no vision, it's important to have the sound on while checking bushes.
Also a thing to note, you can hear (and sometimes see) enemy spells and ward-placements through the fog of war which helps you locate an enemy you have no vision on.
Overall, try to keep the sound-effects on. If you're a person that can't play with music then just make sure that the music isn't too loud so you can still hear the spells/effects of the game. There are also people who play worse without the ingame music which sounds ridiculous but it's a serious matter of habit.