I'm wanting to build a flying wing designed drone and I'm wondering if I were to fill the fuselage with helium if it would improve it's range.
If the end result of the sealed wing filled with helium is lighter than the same wing filled with a normal atmosphere (nitrogen, oxygen, and assorted other gases), then yes - a lighter aircraft will, all else being equal, have better performance and thus longer range than a heavier one.
If you'd actually be able to achieve economic benefit is doubtful - the delta in weight will be offset by everything required to seal the wing up, and the gain in efficiency may be pretty tiny. Beyond that, if mechanics need to access stuff inside the wing, you'll be paying to replenish the helium whenever that happens. Plus, the volume inside the flying wing is normally where things like fuel, passengers, crew, cargo, engines, and etc would go; you may find that you don't have all that much available space left to fill with helium.
This question is interesting as it delves into the efficiency cross over point between airships and aeroplanes.
From history we learn that airships had efficiency advantages up to around 80 knots, but were bulky and hard to control in poor weather.
A drone sounds like something that may fly at slower speeds, so why not cut loose a bit and think about a lifting body hybrid.
Slower flying speeds lend themselves to very thick heavily cambered wings, or lifting surfaces which could be inflatable.
In the end it is thrust/drag expense for lift + thrust drag expense for forward velocity. An airship drone may give you greater range.
To elaborate a bit on Robert DiGiovannis answer, yes certainly that would increase the range, if not for any other reason, than because it is quite easy to make it add considerably to the structural integrity of the drone.
Another thing you need to realize is, that saving weight and other range extending measures can come in a lot of small contributions, rather than one big one. So even if the volume is not all that big, as long as it contributes to the cause, its welcome.