If there are private channels on slack, can a user without admin rights see the list of those channels?
Clicking on "Channels" gives any user a list of all channels, including private ones. The list can be filtered to show private channels only.
A Slack user - including admins and owners - can only see non-public channels (e.g. private channels, direct messages channels, private group chat, etc.) they are of member of.
It's one of Slack's security features that even admins can not see or join private channels of others.