What i mean you cannot check blance of any balance quickly due to lack of index. But you still can do that by creating wallet which contain specific Bitcoin address or master public key. If you add one which already has past transaction, Bitcoin Core will need to rescan blockchain which could take some time.
If you want to protect your privacy, you should download the full blockchain and run your own server and use TOR.
Network >> Proxy >> Use tor proxy at port 9150, Use proxy , SOCKS5 127.0.0.1 9150
Electrum server can know list of addresses belong to same person/group.