Front differential

Being the Armada is available as a rear wheel or four wheel drive, yes you could remove it and still be able to drive it as long as you don't select four wheel drive with the differential out.
However, you would also need to remove the front drive axles and drive shaft. That means you need to make match marks for the front drive shaft yokes.
My question would be, why? If you are removing it for repair and then re-installing it this would work as a temporary thing. If you are removing it because it might give you better mileage, don't bother, there is no real increase there because it's not any real weight involved and you give up the 4X4 ability.