That's a heck of a problem.
Yes, it's running rich because the O2 sensor is getting faulty readings (exhaust gasses are escaping from the hole before the O2 sensor can read them).
Don't drive it until it's fixed (or at least stay out of boost). It defiantly couldn't hurt to try to weld it first. If the weld fails it will be running rich again though, so keep an eye on it. A wide band O2 sensor/gauge would help you with that.
If the weld does fail I suggest getting a new down pipe.