Can a website built entirely in SVG have good SEO?

While text in SVGs are indexed by Google, links may not be followed, and Google does not understand the semantics of the content.

Here is a website built entirely in SVG as a search engine test:

http://svg.nicubunu.ro/

If you type site:svg.nicubunu.ro into Google Search, you can see that only the home page was ever indexed, and it does not even show a description on the SERP. And if you view the cached page, you can see that Google doesn't understand any of the layout of the page.

If Google's advanced crawler is having trouble with SVG websites, I can guarantee that more basic crawlers like Bing and Yahoo will have even greater trouble with it.

So, a website built entirely in SVG will perform poorly in regards to SEO. And aside from SEO, a website built entirely in SVG is much more difficult (or impossible?) to make look good on both desktop and phone browsers.

Let's try some tests on the same website as Maximillian's answer, http://svg.nicubunu.ro/. Both Bing and Yahoo can index the site.

Yahoo Search

Bing Search

My Google search failed to find anything other than the homepage, but Google has stated that they do index svg files. The problem seems to be that Google doesn't follow links in svg files (first result for "google doesn't follow xlink"). Relevant tweet.

I've search around a bit, but there doesn't seem to be any change that I'm aware of, so it's probably still true. In any case, xlink:href is depreciated in favor of just an href attribute which Google does follow so you should be all right.

Conclusion: There should be minimal effect on how your pages are indexed as long as you make sure your links are actually crawlable. All three search engines were able to find the text on the pages they indexed. I haven't tested other aspects of SEO but neither indexing or searchability seems to be an issue.