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If you have a broken sway bar, it really isn't recommended that you drive the vehicle. If its a rear sway bar, you will feel a difference in the way the vehicle chages lanes, makes turns, etc. If it is a front sway, you will definitely feel a difference in the way the car handles, and it will get worse at higher speeds, possibly causing you to lose control.
Yes, you can, but drive slowly, keep the speed down and you'll be fine.