No.
The Xbox 360 does not use Bluetooth, but a proprietary RF call. The iPad/iPhone firstly has no way of recieving this signal, and secondly no way to hook up the receiver to it. Assuming you could hook up the receiver to it, you'd then have to develop a driver for that so iOS can interpret the input. Only Apple can make said drivers as it is faaaaaar out of the scope of what their released API set are capable of, which mean decompiling lots of stuff, at which point Apple sues you for copyright violations.
Going the clean-room way would be very tedious if even possible, by capturing and anolyzing the calls to and from Apple approved peripherals until you have the understanding on how to implement it yourself.
Assuming you somehow make it to this point without getting sued and in a reasonable time period as to not make all your work pointless by updates, you'd then have to probably jailbreak your iphone and implement your driver