Unfortunately, you can’t add a profile picture when you create an account anymore, so that wouldn’t work - it would just give you the system-assigned one.
The only loophole I have discovered is a website called Gravatar that lets you permanently associate a bio and profile image with your email address across the whole internet, but I haven’t looked into how it actually works, just seen that people have done it. (You would probably need to get a new email address, for one thing.)