The answer is no.
Building a website is just the first step in creating an online presence. A website is actually just like a brick and mortar store. It will require the same amount of promotion to attract people.
Just because you launched a great new website does not mean that your business will automatically show up when you Google it. For that, you need to invest some time and energy into promoting and marketing your website.
Do some research and utilize the tools that your web host provides. Include the address of your new website on everything: business cards, menus, press releases, your email signature, and postcards. Talk about your website on Facebook, YouTube, Linked In, or any other social network. Join local groups that will allow you to add a link to their website.
Search engines will think your site isn’t important enough to list if no one else is linked to your website. Purchase advertising on other sites. Add your website to the yellow pages online listing. The more research you do, the more ways you’ll find to help potential customers find you.