Is a flyback diode needed if there are only inductive components on the circuit (Ex. solenoids)
A MOV or snubber or bipolar TVS will usually extend the life of the relay contact. At 24VAC it may not be  that important. Personally, I would consider a bipolar TVS. 

It won't affect the relay directly, but if the controlling circuitry is poorly designed you may see effects from switching such an inductive load (microcontroller resets, flakey behavior increasing in frequency as the contacts age and so on).