I bet the sign itself serves as search engine optimization. If everybody starts searching for "foo" and clicks on my site in the result set then a reasonable search engine might bump my site up higher for searches for "foo."

That's an interesting hypothesis. It makes sense for the company both as optimization of their web pages for search engines and as making good impression on customers.

Not really, if I were doing this, I'd buy ads for the search term so I can guarantee (within reason) I'm at the top.