The cron system of WordPress is not a real Unix cron due to the PHP way to work and relies on site traffic to work. A site without traffic will have the cron system not working.
It’s possible to trigger the cron system externally, as described on the Newsletter delivery engine page, using the service many providers make available on their control panel or using an external periodic call to a special WordPress file, wp-cron.php.
There are many external services, with different pricing schemes (some are free) which let one to configure such periodic call.
Easy cron have a free plan which seem perfect to be used with the Newsletter specific setup instruction, so you can easily try it without any costs. The free plan should be renewed manually every month. Of course this is an incentive to get a paid plan (servers to keep active a cron system like that cost – I know!) and the basic plan for only 7.95$ per year, it’s perfect.
Not only Newsletter plugin relies on the WordPress cron system: I met many plugin which need that system working smoothly, even WordPress for updated a future posts need it!