Will I get banned if I just muted every single person in the game? I just don't talk to anyone or anything. Just play my game and move on.

I rage easily. I have gotten permanent banned on 6 accounts now. All level 30s and over 1600 elo with over 30 champs each and over $100 spent for each account. Will I get banned if I just mute everyone?
I also make money getting paid to play LoL so that's why I need to avoid getting banned because while I don't have a level 30, I don't get paid.

That won't solve your problem.

You said you would rage at people mistakes and everything, so how will not seeing them talk not make you rage when bottom lane gives up 3 kills before 5mins?

No, you shouldn't get banned for muting everyone. Most bans are from chatlogs.
I think thats a great idea. Your already out 600$ I think you should try something different this time.

I don't think the account he has currently will survive if his entire existence is to troll people with his names alone.

I stopped reading at the first sentence.

Go away. You are not welcome in this game.