No. I always do it (every time I get new tires), and they always try to sell it to you (when you get new tires), but it's a separate service, and hardly a requirement. Balancing is, alignment is not.
Their stance is that since they just did an alignment, it won't be necessary. And that may be, but I think they should pay for their screwup in sweat.
And I agree, they owe me more than just an alignment right now. I don't even feel comfortable driving anywhere of any distance today, so they owe me for screwing up my weekend. I was going to go to Gainesville (VA) to get some Wegmans Dragonwell, but I'd hate to be stuck. It was raining cats and dogs yesterday, and my car was hydroplaning every time I cornered.