Indeed, using an arc welder can thaw pipes. Pipe thawers seem to be little more then high current, low voltage sources after all.
While passing voltage through a grounded conductor may seem dangerous and counter-intuitive, consider that most welders feature floating secondary outputs. That is, there is no potential between either the welding lead or the ground clamp and actual earth ground. Potential only exists between the ground clamp and the stinger.
Now, this doesn't mean that welding with an AC machine is inherently safe - if you have your ground clamped firmly to your welding table, and you're leaning on said table - there is probably good voltage potential between you and the stinger, even through your leathers.
That said, for the purposes of thawing pipes, it is my understanding that usage of an arc welder is frowned upon anymore, and for good reason. Water pipes are not designed to be current carrying conductors - as such all sorts of interesting conditions can result when you apply a hundred amps to them. You may end up with current carried through the earth ground to another section of pipe in unexpected ways, current going through the water heater in unexpected ways, current being coupled to grounded appliances with unexpected potential; all sorts of weirdness can result depending on the particular construction. And god help you if your welder has any significant primary-secondary coupling.
Frankly, I wouldn't personally try it. Too much liability. If I had a pipe frozen between the street and the house, I would pay a plumber. Even if a plumber fixes it with an AC-225 like I have in the garage, I suspect it's worth the cost because I'm also paying for them to eat the liability. My insurance guy is a lot happier if, after the building burns down, he has someone carrying a mil in liability insurance to go after instead of little old me.
Times I've had pipes frozen inside my dwelling, I've sorted it out with a heat gun owing to good access.
