Itís a bit hard to tell from the info you have posted. The 2002 Tahoe has 3 different tow weight capacities depending on which engine and which axle ratio itís equipped with. The most likely is the 5.3 liter V8 with a 3.73 axle. If that is indeed the case then the GCWR is 7400 lbs.
You also donít say what year your shadow cruiser is but the current year weighs in at 5385 lbs. Once you add in all of the stuff like the awning, batteries, propane, tongue weight, etc. you will be pretty close to 6400 lbs. That leaves you with 1000 lbs for passengers gear in the truck, food & gear in the trailer and water in the tanks.
So while you may not be above the trucks limits you are pretty close. No way to know for sure without getting some actual weights.
2011 Chevy Silverado Crew Cab 4X4
2009 210 WBS