I've personnally not run a welder from a phase converter. My father-in-law runs a whole machine shop that way, but his buzz box is ran off 220v single phase. All his compressors, drills, lathes and a bridgeport end mill are all 3 phase equipment and they do fine. I've heard that some have ran welders from these converter without any problems, but I can't say for myself. Some had concerns whether or not it would bother the arc on some high freq. TIG machines, but I can't say if it does or not. There has been much discussion in the past on the forum about these converters, try the search function and check it out.
John Wright