I just tested it for you, Swift applications compile into standard binaries and can be run on OS X 10.9 and iOS 7.
Simple Swift application used for testing:
func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: NSDictionary?) -> Bool {
self.window = UIWindow(frame: UIScreen.mainScreen().bounds)
var controller = UIViewController()
var view = UIView(frame: CGRectMake(0, 0, 320, 568))
view.backgroundColor = UIColor.redColor()
controller.view = view
var label = UILabel(frame: CGRectMake(0, 0, 200, 21))
label.center = CGPointMake(160, 284)
label.textAlignment = NSTextAlignment.Center
label.text = "I'am a test label"
controller.view.addSubview(label)
self.window!.rootViewController = controller
self.window!.makeKeyAndVisible()
return true
}