Please tell me if this would successfully allow someone with a permanent ban to create a new account.

Probably

I'm curious why you're getting downvotes, honestly.

Clear your cookies, local storage, session storage, etc. Or at least for Reddit domains. Particularly if you've ever logged in to your banned Reddit account from Firefox. (But even if you haven't, or if you aren't sure, it can't hurt.)

Also, if you don't want to go to the trouble of making a new Gmail account, it doesn't actually require email verification to use Reddit. (At least not on old Reddit. Not sure about new.) Just make up a Gmail account address and use Reddit.

You might even be able to get away with using a Gmail "plus email address". (Like if your email address is "mickey7@gmail.com", sign up with "mickey7+banevade@gmail.com". You'll still get the emails they send you in your Gmail account if you do that. I'm not sure if Reddit is smart enough to prevent you from signing up if your non-plus email address is banned.)

Also, if you don't feel like getting a VPN, Tor makes things easy for free. You'll have to use https://old.reddit.com/, but let's be honest, you should be doing that anyway for so many reasons.

I just used my other alias on my email account, no VPN's didnt clear cookies, nothing. Had no problems

We know that's you, Brutus.