No, this would not. A center diff is used in full-time systems vs. part-time systems. With the center diff locked, it functions the same as any other part-time (traditional) 4WD system. Power is distributed evenly between the front and rear axles; which wheels get power is up to the differentials at each axle.
If your front diff is open, then both front wheels will spin independently.
Thanks. Haven't owned a full-timed 4wd before and didn't understand what was happening. That makes sense.