There are obvious benefits if your site is listed there. Searchers will inevitably choose it from time to time and you'll get more hits.
I assume that the criteria for listing is that your actual domain name has been searched for a reasonable number of times. Now, I know that the main domain for this site is not yet included, even though it does okay in Google. (For example I'm in the third position for Aussie searches for "seo tips" and I sometimes get 15 hits a day from that one query alone.)
Yet I have two URLs that do appear in this domain suggestion box. Significantly, those two are the ones that I have done quite a bit of offline promotion for (using flyers mostly). I have done next to none for this site. I suspect it's this offline promotion that was the crucial factor.
Why this conclusion? Because lately, after having done flyer campaigns for these sites, as well as seeing direct "type in" clicks, I've seen quite a few clicks coming from searches for these domains.
Clearly people are getting savvier in their use of the internet. Upon receiving a flyer they often check to see if the advertised site is listed in Google (which will give them a sense of its quality). Google helpfully shows them a preview as well. If they feel the site is worth clicking on then they will do so. Consequently that hit is recorded as resulting from a search for that domain.
It seems that if you rack up enough of these "URL-search" hits, Google will include your domain in the drop down suggestion box. Given that Google is becoming more and more localized in its presentation of results, I suspect that it will give URL suggestions related to the location of the searcher. So, this seems to be another way in which offline advertising can help with local SEO and bring more visitors to your site.