Yes, you can remove the front driveshaft and drive it without issues BUT that wont help the tcase leak.
If you decide to remove the shaft and it's still full time 4wd (not converted to part time) then you'll need to run the tcase in "HI LOC". Without the front shaft the regular "HI" position will send power to the path of least resistance (the missing front shaft) and the truck wont move.
I'm assuming the leak is pretty bad or you wouldn't have made this post. If you have to pull the tcase to reseal it you might consider adding a part time conversion kit to reduce parts wear and possibly gain a mpg or 2.
Btw, welcome! What part of Alabama? I'm down at the bottom.