[PrBlahBlahtson]

Medically speaking, it might in spirit, but not an awful lot before complications set in and nowhere near the speed you see there.

If you somehow kept a woman that was producing a normal amount of milk from somehow releasing it, there generally will be swelling after prolonged amounts of time (many many hours, perhaps even days). There will also be discomfort and tenderness from this as well. And by normal amount of milk, I mean the amount you'd see from a woman that was breast feeding, not a teenager in puberty that happens to produce a drop or two if you reaaaally work at it. It would also take something with substantially more containment ability than a string.

Also note that this is all taken from layman's understanding of how the entire system works. I'm not a doctor, nor am I an expert or a female.