Who cares about duty cycle on a 120-volt MIG when welding a nut onto a 5/16 or 3/8 stud cannot possibly take more than thirty seconds at a time?
I had a 120-volt MIG for a few years. I was not satisfied with it, and the best thing I ever did to upgrade my welding skill was to get a 240-volt machine...but for this, I don't see how it matters. You're not making a pretty weld-bead, you're firing wire into a single spot, which would concentrate the heat available.
But if you've already started drilling, I don't think you have much choice but to drill all the way down, and pull out the bolt threads. Clean up the threads in the head, if they're in good condition. If not...drill oversize, and helicoil.
Based on the external rust on that head, I bet you're going to drill those studs to the bottom and helicoil.
For the record, just today I had to weld bolts onto a broken stub of a bolt, to unthread the broken piece from a Ford steering box. My buddy was driving along, and suddenly the steering wheel "just spun". I'd warned him that only two of the three bolts were still holding the box to the frame, but he "needed the truck" and didn't seem to care that the steering wheel was a half-turn away from level.
One broken bolt spun right out with a vice-grip and harsh language. One broken bolt had to be drilled, it was totally seized in the iron steering gear. And the third got a series of bolts welded to it, and progressively backed-out. My initial mistake was using 5/16 bolts welded to the 7/16 stub, it would only turn so far before the welded bolt itself broke. Eventually I wised-up and welded a 7/16 bolt to the 7/16 stud, and it backed out with some difficulty. Did a great job of saving two of the three threaded holes, the other will need a nut on the back to properly secure a slightly-longer bolt.