It is indeed possible to see addresses where ballots were mailed, and I was able to view a politician’s information using only their name and date of birth gleaned from Wikipedia.

I’m sure this information can be found in any number of ways, however. There is also a disclaimer stating “ If your information is confidential or you are not yet 18 years old, contact your county elections official to confirm your registration status.” which indicates using that site to register has no implication of privacy.