An AC arc welding transformer is designed to give a reasonably constant current at any particular setting. If the arc length is varied, the volts go up or down to control the current. The set is said to have a drooping characteristic (oo-er!). So the output is not regulated, unlike a close coupled power supply transformer, where a good design will hold the voltage within about 10% for any current drawn within its rating. Rectifying and adding capacitance will smooth the output but if the load drawn is varied the voltage will also vary. If your load current is reasonably constant you should be OK. It will be very interesting to see the results of your experiment. I am not an electronics expert but did sell welding equipment a long time ago.
Good luck!
Ian