No, Wii Sports Resort requires Wii MotionPlus capability for each controller used to play. This can be done either via the Wii MotionPlus Accessory, which connects to the normal Wii Remote, or through a Wii remote with built-in MotionPlus capability.
The sensor in the MotionPlus devices supplements the accelerometer and Sensor Bar capabilities of the original Wii remote. This allows the controller to perform more actions. Remotes with built-in MotionPlus capability are called Wii Remote Plus. These allow players to use peripherals like the Wii Zapper and Wii Wheel without having to first remove the Wii MotionPlus attachment from the Wii Remote.