No bad struts will not cause vibration of your vehicle so it's something else that is causing the vibration of the vehicle.
Bad struts on your vehicle will cause your car to basically float because they are no longer damping the low-frequency oscillations of the coil spring.
Having bad struts can also cause popping noises when steering as they control your vehicles steering and bad struts could also cause your tires to lose contact with the road which is a dangerous situation.
The entire car will also be more bouncy with bad struts and not have vibration.
Most commonly the cause of a car vibrating is due to bad or out of balance tires that cause the car to vibrate and could also cause the steering wheel to shake.
Warped rotors are also another common cause of car vibration or even a bent wheel on the vehicle.