Does the inhibitor obelisk from EnderIO use energy?

Yes the Inhibitor Obelisk uses Redstone Flux (RF)

There are many reasons your obelisk continues to work without an active power supply.

First, the internal power buffer could be full. This is like an inbuilt battery inside the machine.

If that is empty, and the obelisk is still functioning, it could be passively being powered. Ensure that there aren't any wireless RF transmitters nearby.

There could be a capacitor underneath the obelisk - somewhere all of us often forget to check. Machines can also be powered by each other, so even if your machine doesn't have its own power cable, if a adjacent machine is receiving power, it can pass it's power to the obelisk.

Finally, your obelisk could be bugged out - This can be fixed easily by breaking and replacing.

Feel free to reply/edit.