There was a good question I saw in my last post: "Why could the play & charge cable not be designed to transmit information over the cable?"
For those who have not been initiated, the Play & Charge Cable can be used with an Xbox 360 Wireless Controller to charge the battery pack and play at the same time. However, when it's plugged in, the controller doesn't behave any differently - it's still in wireless mode.
I would answer this question by turning it around: what advantage do you get from transferring information over the cable versus wirelessly? Having the cable plugged in means you are close enough that you are not out of range. The response times are the same. The data is not any more reliable.
Let's look at the disadvantages of having the controller in wireless mode when it's plugged in. Primarily, it takes longer to charge the battery - only if the controller is actively being used. Since you're using the console, the time it takes to charge shouldn't matter all that much. It would be a little bit longer before you can disconnect it and go back to being truly wireless, but hopefully you're too addicted to the game to notice 🙂
I think you can see either way, you would have had the same experience with the controller. The play & charge kit could have been used to transfer information, but it doesn't make much sense to do so.