Possible, yes, but it would get you nothing but a dead controller at best, and a fried MCU at worst, but I'll still take the $200.
The XB1 controller uses a Common Ground layout for the buttons, and the Sticks are still the 10k POT style, but that's about where the similarities end. While the MCU in the 360 CG version controllers, as well as the one in the new XB1 controller, are both 100 pin 14mm QFP, they are physically swappable, but, they are nothing at all alike in terms of pinout and how they work.
If you're after a 360 controller that's in the XB1 controller shell, that would have to be done via..
Some type of Adapter
Hack up a wired CL and solder it up to a stripped down XB1 board (end up with a wired controller then)
Redo the XB1 PCBs in the layout for the 360 CG parts (expensive, but also fun, and is how I did the last 3PS60 I made, Wired 360 controller in the PS3 controller shell -
http://i50.photobucket.com/albums/f320/RDCXBG/3PS60_V4/3PS60_BETA9.jpg)
If you meant swap a Viking chip from a 360 controller over to the XB1, then no, same thing applies, the chip would actually fit on the XB1 MCU, but nothing at all would line up to work right.
I have both boards from the XB1 controller scanned now and mostly traced out as far as the buttons and such go, and I've also finished off a first draft of a schematic for the thing. The schematic is for personal use and will most likely never see the light of day, but the board scans will be posted up with more info when I'm finished with a few more things on them.