A half-ton Yukon XL should be able to handle 4,600 lbs straight from the factory.
I can't see the 2005 chart, but the worst-case combination of drive type and axle ratio in the '08 model still produces a tow rating of 7,000 lbs (4x4 with 3.73 axle ratio.) It goes up to 8,200 lbs with 4x2 and 4.10 gears.
If you have a 3/4 ton chassis, the minimum rating shoots up to 9,300 lbs.
The 2005 Yukon chart will look slightly different, but only by a couple of hundred pounds. Check your own truck's owner's manual in the trailering section to confirm. If you don't know your axle ratio, assume the lower number.
GM engineers are very careful about these tow ratings, and they always build in the cooling capacity necessary to do the job up long, steep grades in the desert, in summer. Climbing Townes Pass in Death Valley at 110 or 115 degrees is part of many tow rating test procedures.
The trouble comes when people tow too much weight. Many people never weigh their rigs and wind up over the limit. Failure to check and maintain radiator and transmission fluid levels is another problem. Transmission fluid should be drained and replaced more often if you tow a lot.
Since you don't seem to be anywhere near the tow limit, even if we add-in the weight of luggage and passengers, I wouldn't worry about adding a cooler in your case. Adding one wouldn't hurt, but to me it seem an unnecessary expense. And if it isn't installed right, there can be leaks or the new cooler can obstruct the other radiators already there, harming their efficiency.