Can I create a WatchKit app without a storyboard (entirely in code)?

Yes, It's possible now with Xcode 12.2. We have to choose 'SwiftUI' interface and 'SwiftUI App' life cycle when create new Watch app target (for both 'with companion app' and 'independent' app)

If you read the WatchKit programming guide you will see that you app is actually executing on the user's iPhone and the app sends information to be displayed to the watch by WatchKit.

As there is none of your code executing on the watch itself, you can't perform programmatic layout - WatchKit uses a Storyboard to provide the layout and render the information provided by your app running on the iPhone.

Apple has said that it will be possible to develop native Watch applications in the future, so it may be possible then.