Yes. All it does is construct a URL to United's site with the appropriate date parameter; United.com just looks up and displays the status information. You can look all the way out to the end of the schedule.

However, sometimes the query will fail; I think it's due to a timeout on United's servers, as they're not terribly worried about performance of flight status pages for far future dates. That's why you may need to try several times. Eventually, though, it will load.