Does an image's filename affect its SEO?

Yes. It's probably more so when alt text isn't present, just because Google seems to put a lot of emphasis on that.

Give your images detailed, informative filenames

The filename can give Google clues about the subject matter of the image. Try to make your filename a good description of the subject matter of the image. For example, my-new-black-kitten.jpg is a lot more informative than IMG00023.JPG. Descriptive filenames can also be useful to users: If we're unable to find suitable text in the page on which we found the image, we'll use the filename as the image's snippet in our search results.

Source: Google's Image Publishing Guidelines

Even if this didn't help with seo, though, it would help your users, because a detailed file name such as red-mercadese-slk.jpg will help them a lot more when trying to figure what the image is about than, for example, image.jpg.