@john_wdl interesting idea. And before I say anything else, thank you for adding YARPP support to your theme! :)
Here's the code you want, where yarpp-template-bundled.php is the YARPP template in the root directory of your theme:
yarpp_set_option('auto_display', false);
yarpp_set_option('use_template', true);
yarpp_set_option('template_file', 'yarpp-template-bundled.php');
and, if appropriate:
yarpp_set_option('rss_use_template', true);
yarpp_set_option('rss_template_file', 'yarpp-template-bundled.php');
There's a question about when this should happen, though. If YARPP is installed first and then your theme is activated, it may seem surprising that their YARPP settings were changed (if you don't tell them), particularly as switching back to another theme won't revert these options (unless you build that, but that seems like much).
Also, to check that YARPP is installed, you should check defined('YARPP_VERSION') and probably version_compare(YARPP_VERSION, $supported_yarpp_version) !== -1 so you just don't support older YARPP versions.
Hope that helps!