If you do not publish your connector in the Connector Gallery, then any user of the connector will require read access to your Apps Script project. Without read access their Looker Studio account will not be able to read and execute the script. You do not need to share the script link with the users, only ensure they have read access to the script.
The recommended way of providing access is to enable link sharing for the project. When shared this way, the script will not show up in your users' Google Drive.
If you only want to share your connector with a selected group of users, you can share the script with specific people. When shared this way, the script will show up in your users' Google Drive and they will be able to access it directly. This approach is only recommended if you want to share the script with a selected group of users.