Well, that might be a complicated question and answer. In theory a four bar rear suspension works just fine for going around corners but it all depends on the details. You'll need some sort of panhard bar to keep things in place if the four link is all parrallel. Drag suspensions usually aren't designed to be dual purpose so you might be a little screwed from the get go.

If you put some decent sized tires up front with a large anti-roll bar then you should be able to move the weight transfer back towards the front. Drag cars are usually set up so that the rear has all of the traction. That works great for drag racing but not so good going around corners. The more you shift the traction to the front though the worse you'll do at the drag track.

Drag cars and road race cars do share a lot in common though. Lightweight, stiff chassis, CG towards middle of the car, etc. It is just the tuning on each end that throws a wrench into it.

Best setup for a car that goes fast at the drag strip and the road course is something like a Porsche 911. Rear engine, big rear tires, big brakes, stiff chassis, lightweight car, etc.