I get the feeling that you have already decided to do it, but are just hoping someone will say "You're all good". With that in mind, let me note a few things. I agree that your truck is not an issue. Everything behind it is.
I don't know about "most states allow it". At least one internet sites says that 13 states allow it. Another says that 28 states either allow it or don't forbid it, but quickly go on to say that these states have different limitations on the rig, and requirements on the driver. And these requirements are not necessarily the same as those on commercial 18-wheel triple rigs. It is up to you to be familiar with the laws in each state that you pass through, of course. You should probably check your insurance policy as well.
Your boat weighs about 1700 pounds. Does that include the weight of the trailer? Fuel? Toys? The hitch weight of the boat trailer could be well north of 300 pounds. When you put that weight on the rear of the TM, it reduces the TM's hitch weight on your truck, making the TM lighter in front than was intended by the TM designers. Of course this will create a tendency for the TM to sway. TMs by themselves don't sway, and of course the commercial big-rig triples you are familiar with don't sway. Will your proposed rig sway? I don't know, but I don't want to be around if it does.
If U-Haul installed the hitch, I'm pretty sure it means you don't have a South Dakota TM. Previous TMs (Tennessee and Nebraska) offered an optional rear hitch receiver for a bike rack, but it was strictly limited to 100 pounds of total weight. I don't know if that was a weight-and-balance issue, or a strength issue. As others have indicated, you must know not only how U-Haul attached the hitch to the TM frame (which they can tell you), but how much strength the TM frame has, including things like its own hitch coupler (which U-Haul can not tell you). By the way, does your TM have a swing hitch?
My South Dakota TM has a factory-installed 2-inch rear hitch receiver. The receiver is welded to a 2-1/2 inch square steel tube. The ends of the tube are welded to steel plates which are bolted to the TM's left and right frame members. Right beside the receiver is a sticker saying "WARNING - NOT SAFE FOR TOWING". It this sounds like your U-Haul hitch - and I bet it does, it is quite a common arrangement - you might want to call the TM factory and ask for some details.
Finally, I'm thinking that in a situation such as you describe, you will probably be taking a lot of "stuff" with you. BBQ grills, tents, outdoor rugs, water toys of all kinds, coolers, food and drinks for several people. As long as you carry all this in your truck, that's OK. But if you carry it in the TM, in addition to the hitch weight of the boat, you can quickly exceed the max allowable weight of the TM running gear - tires, axle, etc.
One of our long-time Forum members, Mike Laupp, had a bad experience when a dealer tried to tow two TMs behind his truck as a triple. The whole rig apparently began to sway and went off the road, destroying Mike's TM. You can use the Forum Search tool to find his story and get some details if you like.
I'm not an expert but I am a skeptic. Good luck, and let us know how it works out.
Bill