When you streeeeeetch a band, you STORE elastic energy in the band, so the more it is STRRRREEEECCCHHEDD, the more energy stored, and then when you let it go, the stored energy is transformed into KINETIC energy. Now, the kinetic energy is proportional to velocity squared, so the more stored energy, the fast and further the rubber band travels!

Good question,
The simple answer is yes. The farther you pull a rubber band back, the further it will fly.

This is true unless the rubber band is pulled too far and begins to break. A rubber band is made out of millions of little chains known as molecules. These chains are very small and you can't see them but are what your rubber band is made out of. When you pick up your rubber band, these chains are tangled together sort of like individual strings of spaghetti in a bowl of spaghetti. As you pull back on your rubber band you begin to untangle and straighten out these chains. However, these chains do not want to be straight, and so when you release the rubber band they will tangle up again. This re- tangling of the chains makes the rubber band contract and shoot off your finger. If you pull back more, the chains will be straighter and when they contract they it will make the rubber band shoot off your finger faster which will make it fly farther. However, If you pull back very far you can make these chains very very straight and they will look sort of like uncooked spaghetti coming straight out of the box. Now imagine you took that spaghetti straight from the box and pulled on both ends, eventually you will pull it far enough that the spaghetti strands won't be touching anymore. The same is true with the rubber band. If you pull back to far you will begin to separate the chains, and then your rubber band will break.

Bonus: IMPORTANT: never shoot a rubber band at someone!!! To make your rubber band fly farther without necessarily pulling back farther, stretch the rubber band between your left thumb and pointer finger. Then with your right pointer finger pull on one side of the rubber band and release it from your left thumb. You should now have the rubber band between your two pointer fingers and one side of it should be much stiffer than the other side. Now release the rubber band with your back pointer finger and let it fly (again, do not shoot it at anyone). If you were able to get one side stiffer than the other, it will spin through air and this spinning will make it fly farther than normal.

The more a rubber band stretches, the more energy is stores. When you let go, the rubber band releases the stored energy. As a result, if the rubber band is stretched further, it releases more energy and thus goes further.

In terms of shooting a rubber band? Yes - the more you stretch it, the more energy you store in the rubber band's stretching. When you release it, that energy is translated into motion.