One of the problems that can develop when the center differential viscous coupling siezes up is that the front and rear drives bind against eachother. If a tire or tires on one axle has a larger or smaller circumference than the other axle, the difference in rotation will not be relieved by the center differential. What happens is that both the front and rear ring and pintion gears are under excessive load. The front ring and pinion gear oil is cooled by the engine and transmission thermal mass. However, the rear drivehousing does not get much air cooling; the oil can over heat; and in some cases the rear oil catches fire.
So I would not take this on a long drive until the center differential problem is resolved. If you do take the trip, stop after 40 miles and ascertain the temperature of the rear axle drive housing. Be careful because if my be burning hot. You might be able to smell the oil vapors venting.
Hope this hellps.