I'm gonna stick my neck out and say no (probably) with the current crop of drivers. With long parallel cables, an effect known as bit slew is experienced. This is where the bits of data travelling along the wires travel at different speeds (due to manufacturing tolerances on the wirese). Higher quality cables have less of a problem with this. Serial has no problem with this since all the bits just follow each other down the single wire (line driver capability/source impedance is then the issue, which dictates cable length, along with cable impedance/terminated transmission lines).
Generally the drivers are tuned to be fast (certainly true of the drivers I've written). This means speeding up the data timing to maximise throughput). I have no doubt that it could be made to work by dropping the speeds. Data is latched into a 44780 by a single latch signal, and so by setting up the data and waiting a while for it to settle before latching the data, a long distance connection could be made to work.
Then you have interference and voltage drop along the wire, although I wouldn't expect this to be a problem with a decent shielded cable.