If you're going to hook a inverter up to your welding machine battery, using the machines alternator to make the power (and I realize you originaly ask about converting welding output to current to power your house, I don't think that's feasable and all of your advise has been to mount 12v to 120v inverter on the welding machine), You most likely have much greater capacity in your truck than your welding machine. Your truck (most likely) has a much larger alternator and much larger battery(s) (especialy if you have a later model diesel truck)than that SA-200 so if you intend to go that route you'll probably get much more bang for your buck hooking up to the trucks charging system.
One (very good) benefit of going that route is that you can hook your truck driven inverter to a couple of magnetic oil pan heaters when the cold weather sets in and by the time you get to work your welding machine will turn over and start a lot easier, specially at below zero temps when some guys are running their battery down trying to fire up.
JTMcC.