How can products with images be displayed first in category or filter for an entire collection? (list.phtml)

Question

Magento store owners with thousands of products will no doubt have difficulty getting images and descriptions for every single product. To try and overcome this myself, I found some code that would allow products that contained images to be displayed first.

$this->getLoadedProductCollection()->setOrder('image'/*or small_image*/, 'desc')

The problem is, it only moves product images first per page and not the entire product collection.

Example: Total of 50 products, 30 contain images and descriptions, the remaining 20 do not.

The desired result would be: if the page sorting was done by 10 products per page, the first 3 pages would contain all the products with images and descriptions followed by the remaining 2 pages of products that do not.

How can products with images be displayed first in a category or filter for an entire collection?