Some systems don't support asynchronous printing, but those that do will return [gtk.types.PrintOperationResult.InProgress] as the status, and emit the [gtk.print_operation.PrintOperation.done] signal when the operation is actually done.
The Windows port does not support asynchronous operation at all (this is unlikely to change). On other platforms, all actions except for [gtk.types.PrintOperationAction.Export] support asynchronous operation.