I had a Traverse (2010) without the tow package. The package added the heavy duty radiator, transmission cooler, wiring harness for the brake controller and trailer wiring, tow/haul switch to change the shift points, and the hitch. I towed my 2000 pound popup with no trouble. Yours will weigh a little more. If you visit the Traverse forums, there are folks who have added most of the equipment to get those features. You might have to buy the wiring harness to add a brake controller though, there's no easy way to get a brake signal without splicing into the wiring. There's no brake light switch on the brake pedal, trust me. It uses a brake pedal position sensor and the body control module provides the brake signal for the brake light and trailer harness.
I had brakes on my popup since I had previously towed it with a Honda CR-V, but never got around to installing the brake controller on the Traverse. I just used a T connector from eTrailer that installed behind the taillights to get the trailer lights.