Yes. They would need to click the “I forgot my password” link on the Discourse login form to get a password reset email sent to the email address they use on Twitter. After doing that they would be able to log into their account with a password.
It would be a bad move on Twitter’s part to start charging for their authentication API - logging in via Twitter requires you to be logged into Twitter. They should see the benefit of that. If they start charging for adding a login via Twitter button on external sites, I’m sure someone here can provide instructions about how to customize a site’s login form to help users with the change.
Edit: when Twitter banned links to other social media platforms and then walked back on doing that, I abandoned my plan to build a Discourse site that used tweets as the starting point for Discourse topics, so I totally get the concern about this.