no, 120hz processing on your tv can not be "turned off." 120hz refers to the frame refresh rate, that is simply how your HDTV operates. Sort of like the resolution. If you have a 1080p tv, you are ALWAYS watching 1920x1080 lines of resolution, regardless of the source (standard def, dvd, blu ray, 720p hd cable, whatever), your tv will ALWAYS upconvert the signal to its native resolution...for 1080p sets, that resolution is 1920x1080.
Same thing with refresh rate. Your LCD likely has a rate of 60Hz or 120Hz. Regardless of the signal you input into the tv, your tv will ALWAYS process the frames at 60 or 120Hz, depending on your tv. This is why 120Hz is so critical....it basically eliminates extra processing or duplicate frames that result when a 24hz signal is displayed on a 60hz set. 24 is not a multiple of 60- the tv has to implement a process called "3:2" pulldown to display 24Hz content.
so the end result is that 120Hz is a BIG DEAL when watching blu-rays. Most blu-rays will output at 24Hz, so your 120hz tv doesn't need 3:2 pulldown (which causes judder because extra frames are inserted to even the ratio). A 60Hz set needs 3:2 pulldown to display 24Hz content, so it will not appear as smooth as it would on a 120Hz set.
But its critical to note that most cable tv sources, even HD cable, are broadcast at 60hz. thats why live tv appears smoother than films or blu-rays regardless of whether your tv is 60 hz or 120hz. A 60hz tv will process HD cable sources just fine, no 3:2 pulldown or extra processing occurs. the only real benefit of 120Hz vs 60Hz is noticed when watching sources that output at 24Hz....mostly blu-rays...maybe Dvds, not sure