Can you serve W3C validation logos from your site?

Yes, you can
W3C validation logos can be downloaded to the image folder of your website and served from there. You can edit the associated html code to serve the image from within your site rather than creating a DNS query.
Advantage of this is faster page loading and optimized performance by reducing one DNS request.
N.B According to the Terms and conditions of W3C you are not allowed to edit the images in any way. You may just serve the images as such.