In reply to Jeffrey.

The library that WordPress uses can handle bcrypt hashes. WordPress core goes out of their way to prevent the library from using it during hash creation, but it will fallback to it during verification.

If any of that was confusing, then I'll put it simply: No, it will not mess up your logins. They will continue to work even after removing the plugin. But the next time you create/change your password, the bcrypt hash will no longer be used.