Technically the JK can still get a little bump steer even with the drag link flip and relocated track bar brackets. Though normally it is minimal to none. Reason is, the track bar and drag link are not the same lengths. So when they are level nothing is noticeable. But if you were really leaned over, they are no longer parallel with each other because the lengths are not equal.
Again you'll probably never notice it but technically it could be there.
Steering dampers don't do NOTHING though. Even with a brand new axle, wheel bearings and steering parts, the jeep handled great. But a good steering damper still firms up the steering and reduces feedback in the wheel.
The original poster however would likely be much better off improving other steering parts at this point. ALL of the stock parts are extremely weak with 35s. Crappy ball joints and tie rod ends with plastic sleeves, soft rubber bushings on the track bars. Even the drag link, tie rod and track bars will visibly bend and flex when turning the wheel with 35" tires. The factory mounting brackets are weak, the bolts are threaded the full length (which destroys the bushing sleeves) and undersized which allows movement and the holes get ovaled out. The steering boxes are weak with a single bearing supporting the sector shaft. All of these can be fixed if you spend the time and money. But a steering damper isn't going to fix all of those issues. It may mask some but only for a while.