You can absolutely do that. If you want to upgrade to a paid plan to get some of the features you want, then you can switch at any time through the My Products option in your account or with the help of a GoDaddy Guide. Once you upgrade your site will have all the same customizations and work that you've already put in place, just with the added features. See Website Builder plans and pricing for more info.
You can also do this search: site:BobsFlowers.com and if nothing comes up, there might be a chance that Google removed it from its search engines. Although in some cases, if nothing shows up it just means that the domain name/website did not have content on it ever or in a long, while so Google never indexed it in the first place, so yeah it’s a bit of a gamble.
Stop whatever you're doing and ask yourself this simple question: "Do I need a website?" If your response was anything other than "yes," you need to think again. It doesn't matter if you're the head of a multinational corporation who employs thousands of people or a local mom-and-pop shop from around the way, you need a website to help potential customers find you online. If you have a business, failure to establish an online home is a failure to grow.