Is it possible to take the factory steering wheel audio controls from another car and install them in one that didn't have them equipped from the factory

Not very easily.

Yea, what Mark said. The quickest way to find out if it got the wiring it to take out your radio. Just pop the trim bezzel off around the radio and heater controls. Then remove all I believe 8 screws that hold the radio, heater controls and the small pocket. The 3 components kind of stack over each other. Pull out the radio and look for a smaller square plug maybe taped to the larger wire loom for the radio. If you find it then it could be done by swapping steering wheels and a whole lot of elbow grease.

If that steering wheel control is an ANALOG control system, then when FRONT-FACING the after-market mating harness connector (the NEW GM 24-pin connector) which connects to the mating dash connector, PIN A6 and A7 will be used to connect the ANALOG controlled Steering Wheel controls. Facing that connector, a1 is on the TOP LEFT, A12 on the OP RIGHT, A13 on the BOTTOM LEFT and A24 on the BOTTOM RIGHT. A6 would be the HI signal and A7 is the GROUND. For this to work, YOU MUST INSTALL A RADIO HEAD WITH ANALOG SWC FEATURE such as the XDVD256BT by Dual. If your steering wheel control system is a DATA-BUS system, then you will need to buy an Axxess SWC-1 digital data adapter as well as a radio head with either two leads, labeled SWC1 and SWC GND a radio head requiring. The newer radio heads equipped to accommodate data-bus SW control systems now also furnish a 3.5mm jack on the back.