Yes, you can customize the design to match an existing site design. There are two ways to integrate your own design.
First. You may use the site builder tool to build the design to match your existing site. Go to Design --> Template --> Add. Give your template a name and a description to help you remember what this template is for. Then select Save. This will take you to the template builder where you can create your own design.
Second, more advanced users may integrate their html directly into the store without using the template builder. After doing the above choose the Header/Footer button which will bring up a text box for you to insert your html.
Select the Preview Template button to view what your changes will look like and select the Apply Template button to apply the template changes to your store.