Perhaps the information that would leak is the maximum amount of data that could be encoded in a human readable-format. Someone could then make guesses as to the content on that basis. I do not think, however, that the limited choices per 2x2 block leaks information.
Say I encrypt a series of coin flips, tightly packed as bits "0" and "1". If you guess the wrong key (assuming certain encryption schemes), you'll decrypt something that looks very much like a series of random coin flips -- just not the ones I originally encrypted. So you can't "know" if you guessed the key correctly.
HOWEVER, if I encode the same series of coin flips as an UTF-16 string saying "HEADS TAILS HEADS HEADS ...", it's extremely unlikely that a wrong key will decrypt to a correct looking message. So if the decryption result looks good, you know that you've guessed the correct key.