Is fuelless aviation possible? I've read the article Gravity powered aircraft flies with no fuel. This is making me confusion, as I can not discern if it is credible.
Is it an hoax?
 A: It's a hoax. Think of a submarine—it can go towards and away from the center of the Earth due to gravity and buoyancy respectively, but it cannot do this without changing its density. And it cannot change its density without fuel. From the U.S. Office of Naval Research:
To descend, water is allowed to flow in through the bottom of the submarine:

To ascend, compressed air stored on board is used to pumped the water back out:

If you tilted the fins properly on descent and ascent, you could create forward motion as well. However, conservation of energy demands that any kinetic energy you develop for motion was paid by whatever energy was used to change the density (in this case, you use fuel for the pumps to compress the air and push the water out). The proposed "gravity powered aircraft" would work on the same principal, the only difference being the surrounding fluid would be air instead of water. It would still require fuel to change its density.
A: The Solar Impulse flies without fuel, so the answer to the question in your title is yes.  In theory you could design an airship that used very little energy. It would have to become lighter than air to take off, say by shedding some ballast, fly to where it is going, and become heavier or catch a landing rope to land.  If that sounds like a helium balloon, it should.  If you want to drive it to a place the wind won't take you, you need some energy, but it needn't be much.
A: A blimp or zeppelin can fly without using energy.
If it's engines are turned off, it can travel with the wind.
I think you're asking - can it be done while having control over where you go, or how fast, while using arbitrarily little fuel?
This is an old idea, and it has been tried.
It is possible, but so far not practical.
To find out more, just Google "Deltoid Pumpkin Seed".
