Is it possible? Of course it's possible. Is it smart? That depends on a bunch of factors, a 700R4 is not an idiot-proof transmission. It is quite capable of destroying itself if overheated. And if you don't have a temp. gauge, you're driving blind in that regard. IMO, if you're not able to easily and concisely answer each of
@Blue85's questions (which are basic towing parameters), you're not ready for towing a heavy load. Having "a transmission cooler" is not the same thing as having a
good transmission cooler, and this is not a forgiving transmission if it is abused. You want to have confidence in your equipment before you undertake that kind of trip. Why am I telling you this? Because my formerly driving Suburban has been grounded for over a year now after a very similar towing trip. I took a marginal transmission that I was kinda thinking of replacing and turned it into a crummy transmission that I how hafta replace. Which wasn't great, as I wasn't ready to replace it at that time. So that took a good vehicle off the road.
Will the same thing happen to you? I don't know. But it is certainly a possibility, and it would be prudent to plan accordingly and address the potential issues so they don't turn into real-life issues.