Yes, after I asked the question here I started doing more research and confirmed that mine does have the transmission cooler. I got the part number from Chevy and asked them if there's an available factory upgrade. I was curious because, like I mentioned in my question, you can pay extra for a "Max Tow Package" for Tahoe's, and one of the items listed in that package is a transmission cooler. But I don't know what it gives you additional because mine already has a transmission cooler, and the only upgrades available are after-market.
Armed with that knowledge, I bought an OBD2 adapter that I can plugin to the truck and hook up to my phone because I wanted to be able to see what my transmission coolant temperature was when I tow. My Tahoe doesn't have a transmission temperature guage on the dash (or at least not a standalone guage - more on that in a second). We towed the trailer last weekend down to SC, and I wanted to know what sort of load I was generating on the tranny. I plugged in the OBD2 sensor and it worked great, except that I tried 2 different apps and *neither* of them listed the transmission temp. They both listed seemingly everything else, but not the 1 thing I'd actually bought it to do. I was bummed until I started scrolling through the information page on my dash (between the tach and speedo) and discovered that there was a transmission temperature screen that you can add to the list of information and display! So I didn't need the OBD2 sensor after all, although I kept it because it really does have a ton of other useful data (and I have to think tranny temperature is in there somewhere, I just couldn't find it in either app I tried).
Anyway, like I said, I towed the family and trailer down to SC last weekend and watched the transmission temp the whole way. The hottest it ever got was high 160's, and that's with an outside temperature in the upper 80's. It normally hovered right around 160, which I was very happy with. The road between here and SC is pretty flat, so I understand that going over mountains out west it will undoubtedly get substantially hotter than that, but I was really happy to see that normal strain towing a loaded trailer (probably at least 5600 pounds loaded down, I haven't taken it to the scale yet) on the highway was minimal. That makes me think that upgrading the stock transmission cooler isn't necessary. It's not like I'm towing with it very frequently, and the overwhelming majority of my towing will be on mostly flat roads, so it seems to me upgrading to one of the much larger coolers would just be overkill.
I'm taking a much longer trip with the trailer soon, so I'll have even more insight after that, I suspect, but I haven't seen any evidence so far to suggest that I need to upgrade the transmission cooler.
