Some unsolicited advice....yes, the Hensley or Propride will completely eliminate any sway issues and that Tahoe will tow that trailer as straight as an arrow with zero sway in any and all conditions. I towed a 34' with my Suburban.
Now for the bad news...that hitch design places a lot of stress on the receiver. I twisted my factory hitch receiver like a pretzel with the Hensley. Upgrading the receiver is an easy bolt-on but definitely advisable. Next is the rear differential...GM 1500 series trucks that is a weak like (I had a 2500). Would advise synthetic fluid if he's not already running it and a Mag-Hytec finned extra-capacity cover. Would also strongly advise adding a transmission temp gauge.
Think of it this way....a strong cross wind or load imbalance will exert a sway force on the trailer. The hitch resists that sway force, but in doing so applies much of it to the the tow vehicle.
Wheelbase and suspension stability help the tow vehicle resist those forces, and the Tahoe is at the minimum edge on both of those. If the lack of sway makes in turn makes the driver overconfident about the rig he might wind up in trouble with the Tahoe.
