Can I design a template with a section containing a background image?

Yes, you can. To do this, hover over the section where you want to add the image and click the Edit section layout icon (pencil icon). This opens image options on the left-hand side where you can paste an image URL, select a previously uploaded image, or upload a new one from your computer.

For more guidance, go to Email > Create Email > Step 3: Message Composition.