The take off point will always be 'zero', and during any flying you then do, the altitude that is shown on your flight monitor will be relative to this point. That means that as you descend along the cliff edge - below the takeoff point - the altitude readout will be negative. There is no issue with this at all.
What there could be an issue with - as mentioned above - is signal loss between the remote and copter as the copter descends out of 'view' of the remote. Also, the copter's sky-view could become restricted as it descends along the cliff face, and it could lose satellites that it had acquired in order to establish and maintain GPS positioning, and things could get very interesting then, especially if you could not see the copter.
I'm not suggesting that you don't try what you have in mind, but as Doecliff mentioned above, attempting a flight like this requires a both frequent and close watch on RC connection and satellite count.