Theoretically no, all of your messages stored on Beeper servers are encrypted. But they will get all your metadata.
But I wouldn’t worry about that anyway since Discord not only has access to all of your messages but sells them to companies to process for AI. So that’d be the far easier and faster route for them.
If I’m honest, it’s not convenient either. I stopped using it years ago because I kept getting logged out of my accounts and flagged for “automated activity”. Plus they straight up lie about supporting SMS and RCS. The only “support” they have is connecting it to your Google account.