Arc welders are current limited, either by transformer size, or active semiconductor circuitry. But you can not just short circuit the two electrodes and walk away, you need to momentarily short them and start the arc. Once the arc is going, it is no longer a short but is a low resistance load.
And, contrary to popular belief, you can get electrocuted from the two leads. The open circuit voltage is typically greater than 70 v, which is technically high enough to cause big trouble.