Yes, once the render starts, you can close your browser tab, the rendering process will continue in the cloud, and you'll receive an email when the render is done.
Note: Keep in mind that the high-resolution render of an animated logo will take much longer than a low-resolution render. This is because the quality is higher, and we render it in multiple aspect ratio formats.
Check the following page, "How to Animate a Logo," if you want to learn more about the whole DanceLogo process of animating. For more details or information, you can always contact us. We are happy to help.