If i dont have a steering stabilizer/damper shock would it cause the steering/truck vibrate while driving downt the road?

 

Most likely there is something causing the vibration. The damper would only be able to squelch a certain amount of that so that you wouldn't feel it. Most likely there is an issue with your alignment or balance of your wheel/tires depending on the vibration (maybe brakes too). The damper would only hide it, if at all.