Probably not possible currently. Complications are limited to updating about every 10 minutes (at the fastest.) Unless you open the watch app... You could have a complication that you tap to open the app, then the distance could be displayed right away in both the app and the complication.
Maybe Siri would be the way to go. It could open the app, if one exists on the watch. Although you'd have to talk to your wrist every time you want to see the distance...