Nope, not generally a good idea to put grease in the differential. Although I've taken some apart that the oil had turned to grease--burnt grease at that! One of the reasons it doesn't work is that the gear lube also needs to cool the gears--which is another function of both engine oil and transmission oil/fluid. Grease doesn't allow the gears and other parts inside the diff the chance to cool down as it moves around.
