is the 4200lbs. number from the brochure/website OR from the actual yellow weight sticker on the trailer?
if it's not the yellow sticker number, you can add about 400lbs. for normal so-called "options" that nearly all trailers have. i.e.- spare tire, oven, microwave, awning, air cond. and so on.
so you're at 4600lbs.
now, say your wife weighs 150lbs., which is what the 5200 number is based on being the only thing in the Traverse. before you add the weight of the battery, propane, water and your cargo, you have to subtract your weight and any cargo in the Traverse from the 5200 number.
meaning meaning if you weigh 175 and you've got 25lbs. of cargo, then your towing capacity is now down to 5000lbs.
so, now you only have 400lbs. for battery, water, propane and cargo or you'll be over the Traverse's towing capacity.
can you do it, i guess you could if you only camped in Iowa or Florida. but if you're talking about mountains, then i would definitely advise against it, if you plan on keeping the Traverse for a while.