The only issue with ‘untrusted’ certificates is with browsers and some other clients, such as email clients. The API will not care about the status or presence of a CA. That being said, you can get free recognized certificates from StartSSL.
I gave up using the WP-Piwik plugin in favor of WP Analytics Tracking. What I like about WP Analytics Tracking is that I simply copy and paste the code as I like it in the blank field. This works fine for me with tracking through Piwik, though if you are seeking to view analytics data within the WordPress dashboard, this will not be available with this plugin.