I'm sure the front end would want to keep moving around on you which would make it very uncomfortable while taking turns at any decent speed. There is a reason drag cars don't see much street time and when they do they go slow. Also, skinnies don't do anything as far as your front end handling well out on the streets. To get your car as quck as you can on the drag strip there are many daily driving comforts you must sacrifice. Long winded, but to answer your question. Yes you can drive on the street with no front sway bar, but I wouldn't do it on a daily driver as it would become a safety issue if and when you had to avoid an accident.
I drove my blown 94 gt with no sway bar and skinnies everyday when I had it. No problems driving it on the street. You just got to know youre not going to corner quick. I just ordered the BMR part so I will see first hand how it goes. When you make the sacrifices to go faster in a straight line you have to compromise somewhere. Cant do both...