Yes, having a W3 standards compliant website has SEO impact. It doesn’t make your site rank higher, if that’s what you expected. It makes your site crawl able. W3 compliance means creating HTML (XHTML and CSS) codes that are technically correct, thus making the job of the search bots much easier in scanning them. Everything that makes the job of the bots easier has a positive SEO impact.
But the real value of the W3 standards is for the users: the people who come on your site and get to see it correctly with any browser and any device they might use. Correct HTML has a lot to do with web accessibility. As a matter of fact, they walk hand in hand.
One of the frequent HTML errors highlighted by the W3C markup validator is the absence of ALT attributes for images. The ALT tag was created to describe an image for people who access the Web with text browsers, for the blind and people with other visual imparities and for those who turn off images in their browsers to get a faster browsing experience.
When you include a proper ALT tag to your images, you do image SEO: you optimize your images for both the users and the search and you make one step forward to a valid HTML code.
Now that you know these random facts about W3 standards, do you still believe they are SEO irrelevant?
So validate your website as soon as you can. Optimize those ALT attributes and you will see results in the SERPs too.