If you want Logaholic to be able to detect traffic coming from Google Adwords paid search and see the difference between traffic coming from Google natural search and from adwords ads, you need to turn "Auto-tagging" on in your Google Adwords account.
The parameter used in auto-tagging is called "gclid" and will show up in your landing page URL when a user arrives at your site from your ad. For example, if your site is www.mysite.com, when a user clicks on your ad it will appear in the address bar as:
You can manually enable or disable auto-tagging in AdWords.
To enable/disable auto-tagging: