No, adding coil overs won't affect the torque tube system. The only problem you may have is that the upper shock mounts aren't made to support the full weight of the car. If you use air shocks or overload coil overs just keep an eye on the upper mounts. Too much weight will push the shock through the floor. That was a problem on Javelins in the 70s with kids putting on air shocks and jacking them up, but the mounts on your old Rambler are a bit stronger -- though they are still not designed to carry the weight of the car.
You might want to investigate air bags though. Not to replace the springs, but that fit INSIDE the original springs to stiffen ride or increase load capacity. Coil over shocks don't cost any less. See AirLift 1000 | Air Lift Company – Tow and Haul with Safety and Comfort
You will have to call them, as there is no listing for Ramblers. They made them years back, and should have one that fits the spring. Ask to talk to someone in the technical department if you have to. Another option is their "Ride Control" product (RideControl | Air Lift Company – Tow and Haul with Safety and Comfort
). You need something that would bolt to the top of the axle and the "frame" rail.
You can also roll your own, or simply replace the rear springs with air springs. You don't need a compressor or air tank unless you want to adjust the ride on the go. Simply install an air hose out to a manual air valve mounted somewhere you can get to it with an air hose. Put the same amount of air in each with a good gauge. You might need to put a little more in one than the other to level the car side to side, but it won't be much. The air spring (or more commonly called "air bag") isn't expensive -- the air compressor, tank, and controls are. You don't have to have them though!
Finally, consider just getting new springs. They will run about $200 a pair. As you noticed, it's softly sprung. All 50s and even early 60s cars are like that. There were few roads where sustained high speed (over 50 mph for more than an hour) travel was even possible at the time. Most roads were rougher and soft suspension was needed to absorb the bumps and jars. Everyone assumes roads were about the same! The Interstate system didn't start construction until 1959, and less than 50% was ready by the mid 60s.
Order springs from Coil Spring Specialties
. On my early 60s Ramblers I order them 12-15% stiffer than stock. The stock HD springs were 20-25% stiffer. I find those a bit TOO stiff. The Coil Spring Specialties springs are progressive rate whereas the originals were not. Progressives are soft to start with and get stiffer as they compress... or rather the rate increases as they compress. There is little resistance at first, but it increases as needed. This gives a good ride and increases handling tremendously on these old cars! Order new springs 15% over stock all around and the car will handle and ride a lot better. People couldn't believe the change the stiffer progressive coils made in my 63 American (leafs in back, I stiffened them with bolt-on helper springs). The better coils in front helped more than adding a sway bar (which I did, but found there was really no need -- really didn't notice it being there).