There are usually two kind of a consortium networks: the one that was designed as a permissioned network and the other one which is a public network, like Ethereum but it is configured in a consortium scenario. Public networks have however pseudonym visibility by default meaning that all of the transactions are visible on the network, however the real identity behind the keys is not known. This architectural feature will not be changed even if you run your network in a consortium scenario. Your blockchain and transactions will be visible as much as your network is visible. With other words, of you manage to run everything on a sealed network, like with VPN-s and firewalls, it means and increased privacy. If you want achieve more privacy, you have to consider some kind of a encryption on the network, like with zk-SNARKs.