Do heavies go VFR? Absolutely, and not only do they go VFR they do carrier breaks as well.
The US Navy has a "scheduled airlines" that ferries personnel and equipment around the continent. Its passenger line uses DC-9's. I was in Beeville, Texas going through advanced jet training in the A4. We were already in the pattern doing carrier pattern touch-and-go's when we heard a DC-9 call at the VFR initial. We were expecting the following call to be for a straight-in VFR approach, and to our amazement we heard, "Tower Heavy 201 for the break." The tower came back quickly, "Break approved."
This was the coolest thing I have ever seen. Absolutely stunning. This big guy comes in to the field at 800 feet and makes the break! I was cheering in the cockpit watching it.