They do have their own web crawler. I don't have any idea what percentage of their results come from it, but presumably as they grow their own search results will take an ever-increasing slice of the pie.
There doesn't seem to be any evidence that it's used for indexing at all; it seems more like it's just used to scrape additional info from sites that they index via real search engines like Bing, Yandex, and Yahoo.
Their own crawler is not used for any organic search results, only widget stuff like Instant Answers (and spam detection apparently as per sibling comment).
