I have set up an AdWords conversion and put the conversion tracking JS code on a test page.

However, I don't see any conversions tracked when I visit it.

Does the AdWords conversion tracking only register your conversion if you come to the site by clicking on an AdWords campaign?

Google's help page advises me to test the code by clicking a campaign.

However, I would like to use the tracking to track all conversions, not just AdWords. I considered using Analytics as well, but it seems you can only track via url there, not JS, which would mean I had to restructure a part of my page. (Because currently a conversion appears does not necessarily happen on a different URL.)

Is AdWords tracking not a viable solution to track all visitor conversions on my site?