It would be the scan of the column data lines and sequential row update of the LCD that would be detected. For low spatial frequencies where you're simply mapping changes in the image, it might still be doable, but the real challenge is that the resolution of monitors and refresh rate have increased so much that it's more difficult to resolve characters or images. OLED is even more difficult, because the top cathode layer really shields most emissions (much more than the patterned VCOM of most modern LCDs).

Embedded touch is a whole'nuther issue. One could certainly remotely measure the radiated emissions of a cell-phone to get finger proximity and position in at least one if not both XY dimensions.