Any flat panel TV with a composite video input can be used as a monitor for an Apple II -- but beware of "lag" (latency) on the display, especially on HDTVs. Due to the analog to digital signal conversion and "HD" resolution upscaling that the TV performs, a delay of up to 1/10th of a second can be introduced. For text based applications this is unnoticeable, but especially for video games you will notice right away that when you move your character using your keyboard or joystick, the corresponding image on the screen moves a split-second later, and the sound/video synchronization is thrown off as well.
Standard definition (non-HDTV) flat panel TVs have much less "lag" because they don't need to upscale the image to "HD" resolution, but these haven't been sold new in about the past two years.
I have no idea how much, if any, "lag" is introduced by using one of the aforementioned "scan converters," but basically anytime a video signal gets converted from one format to another, this is an issue you have to be aware of.