Yes, it will.

I checked and you seem to be correct, at least for Firefox and Chromium. I tried using:

https://self-signed.badssl.com/

and when I clicked "Accept the risk and continue", the certificate was added to Certificate Manager. I closed the browser, re-opened it, and it did not prompt again.

I did the same thing in Chromium and it also worked, though I'm not sure if Chromium's are permanent or if they have a lifespan of any kind.

I am absolutely 100% certain that it did not always work that way. I remember a time when Firefox had an option to permanently add an exception, but it was not the default.

Either way, apologies for the misunderstanding. I genuinely did not realize that it worked this way, and it runs contrary to my previous experience dealing with self-signed certificates.

To be honest, this mostly resolves the issues I've had with self-signed certificates for use cases where getting a valid certificate might be a pain. (I have instead been using ACME with DNS challenge for some cases, but I don't like broadcasting all of my internal domains to the CT log nor do I really want to manage a CA. In some cases it might be nice to not have a valid internet domain at all. So, this might just be a better alternative in some cases...)