No, I think you are wrong any way you slice it.
First you might be thinking of AA in that it upsamples the textures to a higher resolution, does the average of a few frames and then downsamples it to the resolution the game/3d application is running at. This would work even if the monitor doesn't support the "higher" resolution (which can be above 1600X1200) because it's an internal calculation in the GPU - the display is at the same resolution.
Second, you might be thinking about running the screen at a lower resolution (ie 1024X768 perhaps) and then thinking you will be limited by the monitor's scaling. While this is true and non-native resolutions cannot look perfect since they are scaling the pixels to display a smaller area, this doesn't 'limit' AA in any way; it just won't look quite as good as at the native resolution (although newer panels, ie newer Samsungs have very good scaling algorithms now and display non-native resolutions almost as nicely as native ones (at least in games) ).
I can't really think of a way to put it any clearer, but as Mathias said, AA works regardless of resolution and screen type. The TFT doesn't limit you in any way aside from the maximum resolution you can run being the TFT's limit (ie 1280X1024 on a 17" or 19" LCD).