With Apple TV connected to my HDTV, can I get my Mac to treat the TV screen as an additional display (i.e., not just for mirroring)?

With my HDTV connected to my Mac via an HDMI cable, I can tell my Mac to treat the TV as an additional screen (not just a mirror for what is on my Mac). I can open separate windows on the TV screen that are not displayed on my Mac. I want to know if the Apple TV would let me get rid of the cable from my Mac to my TV, while still being able to treat the TV as an additional display. (I already know I can use it to mirror what is on my Mac.)

Apple TV

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