It would work for TIG, but for MIG You would need to use an ajustable voltage regulator in place of the rheostat. You would need to set the voltage to the proper value for the wire You are burning. For MIG You would be better off re connecting the batteries for 24 volts & using a Ready Welder, GoWeld or other battery MIG setup.
You would do yourself a huge favor if you looked very seriously at a Premier Power Welder. Study the PPW website carefully and then email any questions that you might have. If you intend to be able to actually have your alternator work as it was designed after doing some emergency welding as outlined in this link; pay VERY CLOSE ATTENTION to information therein. However, be apprised that very frequently this type of use will quickly melt down even the best high output alternators. An alternator/control box setup like the Premier Power Welder is designed to function as a engine driven welder. This unit supplies DC power at 120V and DC welding power. I have very successfully welded SMAW, TIG and FCAW processes with this unit. The FCAW work was performed using a Lincoln LN-25 wirefeeder and NR-211 wire. The stick performance is outstanding and the scratch start tig works equally as well. I have one of these on both of my welding trucks as a back-up unit to the full size engine drives I run everyday. Additionally, The Premier Power Welder is awesome at recharging batteries quickly. A limitation that may befelt you with either of these welding power sources as we are discussing in this thread is the fact that you will not be able to TIG weld Aluminum owing to the lack of Hi-freq and the DC current you are producing. You will however be able to stick or wire feed weld aluminum wuth the proper accessories. BTW, The Premier unit TIG welds 304 and 316 stainless fantastic with a simple air cooled TIG torch and Argon sheilding gas. Hope this helps!