so to answer the actual question.
If you use a sling the same length as your arm, then you should - logically be able to get it twice as a far.
Realistically, because you use a completely different technique to use a sling you should be able to get it a lot further than twice as far.
I won all sorts of throwing competitions in my distant youth. Including welly throwing at the camp fete - against much taller kids.
Most british kids spend their youth kicking a ball - I always preferred to throw things.
This question gets interesting when you get a human with ridiculously long arms who is trained to throw.
I've always said if you could have got hold of randy johnson in his prime and have larry bray (himself a baseball pitcher in his youth) train him to sling - he'd have broken the world record with ease.
A skinny 7 foot tall MLB pitcher has arms longer than my arm and a decent length sling combined.
Could he throw further than i can sling ?
With a baseball - absolutely - those things are horrible to sling.
With a smaller, denser missile ? probably not.
So yeah it does come down to the missile being thrown.
But on balance you should always be able to get it further with a sling - as long as you did both throws