Is there an 'infinite cycling loop' in ORAS, similar to the Lumiose City Tower in XY?

Yes!

At the Battle Resort, the camera pans around as you ride around the island. You can hold 'Up' continuously as the camera swings around.

The perfect line is right up against the daycare kid, but the way to start the loop is to go to this point (just to the left of the Pokemon Center):

This way, you can hold 'up' just as the camera pans around, meaning you continue heading left whilst still holding 'up'.

It's more beneficial than in XY, as you have the daycare and the IV checker close at hand as well.

Here's a video showing the process:

Sources

• Reddit
• Personal Experience

There's also one in Mauville City: in the little shops on the walls, if you line up with the top-left corner in one of them and hold down the circle pad at a diagonal down-right angle it infinitely loops.

I don't think anyone else knows about it.