Nope, the SCLogin module doesn't have to be published at all. To login with LinkedIn, the Login With LinkedIn button will obviously have to be displayed somewhere. That can be done by:
* Enabling the SCLogin module (which shows the button and other info)
* Using the {JLinkedLogin} button in an article text, custom HTML module, or hardcoded into a template
We shoot for flexibility and try not to 'lock' you into a specific way to do things!
Hope that helps,
Alex