Can iOS devices be connected to the Thunderbolt port on Macs? I saw an image on a rumor for a new Apple connector to attach the new iOS devices to my Mac using the Thunderbolt port.

This would be great because the one port on my MacBook Air that isn't in use all the time is the Thunderbolt port. The image looks badly doctored, however, and I can't find any substantiated evidence that this product exists.

Is there a way to connect new iOS devices to the monitor port on new Macs?
Nope. I don't know where that came from, but it's certainly not a current product, and it's unlikely to be a future one.

Thunderbolt requires expensive chips relative to other connector technologies, which take up a fair bit of PCB space, which is at a premium in iOS devices and iPods (just look at the iPhone 5 teardown). In fact, reducing the size internally is a big part of the reason they went to the Lightning connector in the first place.

Additionally, chips are required in the connector itself. The Lightning connector is much too small to contain the required chips in their current incarnation (the two connectors aren't to scale in that picture, the Thunderbolt connector is much bigger than the Lightning connector).

Finally, there wouldn't be much benefit to using a Thunderbolt connector with iPods or iOS devices. The flash memory in them is not particularly fast, certainly not to the point that it would come close to making use of Thunderbolt's 10 Gb/s connection. USB 3 is a far more likely evolution for Lightning based devices, and would still provide plenty of bandwidth.