I haven't tested it yet, but from my discussions with people at XBox, the XAC will work with the UltraStik in one USB port, and the Quadstick in the other USB port. You have a limited number of buttons that you can get from the Quadstick, but if you are using the XAC, you can map inputs around and use buttons from the XAC plus external switches. The Quadstick has two digital outputs, so however many buttons they allow in software, you can still connect two more outputs with a 3.5 mm cable to inputs on the back of the XAC.
The Quadstick has three serial connections which can be used for voice commands or sending UltraStik position & button data to the Quadstick via QMP. One via Bluetooth, another via a cable into the IN port, and finally in QMP you can send commands via the USB connection while in some emulation modes.
The Quadstick supports the UltraStik directly in to the USB A port on the back or relayed via the QMP.
Just to make the decision more complicated.... The XBox Console has "co-pilot", which allows two controllers to work together, so you could use the XAC for some things and a Quadstick + CM for others. I don't think co-pilot works on the PC.
If the USB-A port on the Quadstick is not used with an UltraStik, it can be used with a
USB-A to A cable to connect to a second host. (Power always comes through the USB-B port) You could connect the USB-B port to the PC, the USB-A port to the side of the XAC, then switch between the two. You could probably find a program like
Controller Companion to let you use XAC inputs for controlling the PC.