do_action('init') calls any functions that have hooked the init handle. Generally, these are plugins. Removing that will probably make them not work.
Your problem is probably wp_cron being called by init. In 2.1 and up, the cron process is called externally, so one thing that could be your problem is the DNS resolution not working on your webserver to find its own address.
Regardless of that, you *cannot* remove the init action hook. Too many things rely on it. Akismet, widgets, wp_cron, kses... You will find really odd things going on without the init hook.
To find out what is relying on init, search your codebase for
add_action('init',... and find what's hooking itself to the init call.