To avoid, that the Jetpack plugin wants to create a connection to your wordpress.com account, you can enable the Jetpack development mode. When using the development mode, many features are disabled, but some important features (markdown, widget visibility) are available.
To enable the debug mode, add this line to your wp-config.php:
define( 'JETPACK_DEV_DEBUG', true);
If you want to enable the debug mode using a theme or a plugin, use this filter:
add_filter( 'jetpack_development_mode', '__return_true' );