Sure.

Can it be done temporarily? Sure. Permanently, that's a different question. The repeated heating and cooling of the pipe is what caused it to break, much the same way you can break a piece of metal by bending it back and forth. Stainless Steel, which is what that pipe is made of is actually quite soft. Yea, I know people think it's hard becuse they burn up drill bits when they try and drill a hole through it. With proper equipment, and techniques, stainless drills quite easy. Anyway, over time, the metal starts to fatigue and fail just as yours has. When you weld up the crack, you will make that part of the pipe stronger than the pipe around it, and of course that results in failures on either side of the welded repair. The only variable is just how long it takes the next failure to occur.

One imnportant note. Unplug the O2 sensors, and any computers on the car before doing this. Voltage spikes from welding are know to occasionally damage sensitive electronics.

HAZ (Heat Affected Zone) is the area directly on each side of the weld and is a weak area unless the part is properly preheated and a slow cooling process is used, this will greatly improve durability. Pretty hard to do with the part still on the vehicle and if you take it off well why not install a new one. If it were mine I would probably pull my 220volt mig welder with the .023 308 ss wire under there and weld her up every time it broke only takes 10 minutes or so to grind it off and reweld. Do you have several hundred bucks to get setup with the proper equipment and then a few weeks of training/practice time?? that way you can crawl under this puppy every year or so and weld like crazy (real crazy)

john g hit the nail on the head as usual.

The head pipes get hot as the hubs of h*ll. Wrecks the material after a while. Give it a try if you want, but don't be surprised if it cracks again.