Yes, the Scheduler supports double click for events. It has to be enabled explicitly using the eventDoubleClickHandling property.
It’s good to know that when the double click is enabled, it adds a delay before a single click event is fired. That is necessary to distinguish between single and double clicks.
The Kanban component is based on the Scheduler so generally the capabilities are the same, but not all functionality is exposed via the Kanban API. The card double click is not supported at the moment, but I’ve added it to the wishlist and it will be added soon.