There are no guarantees with free submissions. Submitting your Web site is free, but no promises are made. Your site might or might not be indexed, and indexing it might take a couple of days or even a few months.
Certainly, you might try to "ask" Google to crawl your website, but that will put you in a looooong list of websites hoping to get added. The hands-down most effective way to get added quickly is to have a link to your website - somewhere. Now that someone has linked to your website, and Google stumbles that link, your website will be queued for fast-indexing.