Depends on the towing vehicle.
Yes, it is definitely recommended that you disconnect the drive shafts at the differentials. Take some tape to hold the u-joint together and some straps to hold the shaft up out of the way. (I haven't seen the tape mentioned on any of the threads where people talk about disconnecting drive shafts, so not sure if the U-joints have the removable bearing caps like I'm used to or not, so just threw that in. If not, you might still find other uses for the tape)
As for how it will actually tow, it will fight you in the turns.
It is heavy, and will push you around.
If the roads are wet then don't go above 30 if there is any chance of having to brake or turn suddenly, because with zero tongue weight from a tow bar, your rear end will get pushed and shoved all over the place.
If you were only towing it a hundred miles or less and didn't have access to any trailers, then maybe do it and take back roads so you aren't going to fast and less visible. That would only be for a truck that's condition was known, and not off of some 5 minute inspection by the auction yard.
Wanting to drive it 1k miles with unknown condition of the HMMWV, especially not knowing fluid levels in the hubs or differentials, well, I highly recommend against it. It might make it all the way no issues, or it might cost you an extra week and thousands of dollars taking care of an issue that you could have taken care of in your driveway at your leisure later on.
And if you're still considering towing it with the RV, I'd highly recommend against it as the RV, unless it's that one chassis version, is not rated for it.
As for legality, unless you live in one of a couple states that allow it, any towed load over 3k lbs requires, by law, functioning brakes.
I can't stress this enough. It is illegal to tow loads over 3k lbs in almost every state in the U.S. if it does not have functioning brakes. If anything happens, you will be 100% at fault and liable, no matter who or what actually caused the incident/accident.